You know every medication has half life in normal case but when they combined with each other interaction might occurs which eventually  lead to slows down the removal of drug (amoxicillin from the body, resulting in higher levels of this antibiotic in  bloodstream).that  means side effect happened. 

Studies have shown that a three times daily dose of amoxicillin 250mg/clavulanic acid 125mg was introduced, an amoxicillin 500mg/clavulanic acid 125mg dosage soon followed. Research showed that the bacteriological efficacy of ß-lactams is associated with the time that free serum levels remain above the minimum inhibitory concentration (MIC). In animal models of S pneumoniae infection, it was shown that the level of amoxicillin needed to remain above the MIC for 30 to 40 per cent of the dosing interval for maximal bacteriological activity. Based on pharmacokinetic and pharmacodynamic predictions, it was calculated that amoxicillin/clavulanic acid 875/125mg twice daily would achieve maximal bacteriological efficacy against strains with amoxicillin or amoxicillin/ clavulanic acid MICs equal to or greater than 2mg/L but not equal to or greater than 4mg/L, although the 875/125mg three times daily and 1,000/125mg three times daily regimens were likely to have some efficacy against strains with MICs of 4mg/L.

Check the following links for further information

http://www.pharmaceutical-journal.com/opinion/comment/still-going-strong-at-30-co-amoxiclav/11079379.article

http://link.springer.com/article/10.1007%2FBF02113605#page-1

http://jac.oxfordjournals.org/content/52/5/826.full

To achieve the following pharmacokinetic parameters C max 7.5±1.6 mg/l after T max  75±25 min. for amoxicillin and C max  2.5±0.6 mg/l after T max t 61±15 min. for clavulanic acid and AUC 0-inf (total area under the curve) for amoxicillin  1278±172 g.min/ml and 354±66 g.min/ml for clavulanic acid particularly in case of acute infections which is required this combination is supposed to be prescribed BID 

Please visit the following link. Hopes it will be helpful for you

http://www.drugs.com/drug-interactions/amoxicillin-clavulanate.html

Amoxi-clav available in different dosage forms, its was available  as (156 mg/5ml) this dose was given three times daily, but  in order to improve the patient compliance the manufacturer modified this dosage form to twice daily doses. Patients feel more comfortable with least number of doses per day and this motivate the pharmaceutical company to look to improve the dosage forms.

Combination generally prescribed twice daily but not always. The pharmacokinetics of amoxycillin and clavulanic acid matches with each other. Moreover clavulinic acid is not antimicrobial as such rather it inhibits enzyme which degrades amoxycillin in the body before its action supervenes. Therfore if only amoxycillin is prescribed then we need to give it more frequently i.e thrice a day, but if combination to be given i.e with clavulanic acid then more of amoxycillin is available systemically without degradation to produce antimicrobial action. Individual factors also play role in deciding frequency of any drug prescribed.

Firstly, the half-life of amoxicillin is about 60 minutes and not 8 hours!  In terms of dosing, the underlying general principle is that the lower therapeutic dose of amoxicillin is administered three times daily (t.i.d) and the relatively higher dose is given twice daily (b.d.), so as to provide plasma levels above MIC (Minimum Inhibitory Concentration) values.  Augmentin (Amox +Clav. acid) DUO formulation contains higher dose of amoxicillin and hence given twice daily.  The actual selection of dose would depend on the indication for which treatment is given.

The half-life of amoxicillin is 61.3 minutes. Approximately 60% of an orally administered dose of amoxicillin is excreted in the urine within 6 to 8 hours. Detectable serum levels are observed up to 8 hours after an orally administered dose of amoxicillin. 

Despite the short half-life, twice daily dosing at the higher dose provides adequate amoxicillin concentrations for 30-40% of the twelve-hour dosing, a PK-PD threshold that has been shown to correlate with efficacy. There has been a lot of work in this area but there is a nice explanation in this pub:  http://www.ncbi.nlm.nih.gov/pubmed/18754699

In agreement with the colleagues answers and beyond PK/PD calculations, the reason to prescribe BID instead of TID is given by the outcomes of the clinical studies which show satisfactory efficacy and safety with BID. Prescriptions to patients are based on clinical studies only.

you have a very logical question .Adding clavulenic acid does not change the pharmacokinetic profile of  Amoxicillin .I would like to see the results of clinical  studies with PK/PD outcome..

Initially the Amoxicillin/Clauvalnic Acid (Augmentin brand) was introduced as thrice daily dosing and subsequently the BD (Twice daily ) dosage formulation was introduced based on the PK/PD calculation. For full understanding of the PK/PD studies please refer to the study :Journal of Antimicrobial Chemotherapy (2004) 53, Suppl. S1, i3–i20 DOI: 10.1093/jac/dkh050

I have reproduced some of the statement which are relevant to the question @ Initially, the adult formulation of amoxicillin/clavulanate was introduced as Augmentin at a three times daily dose of 250 mg of amoxicillin (as amoxicillin trihydrate) plus 125 mg of clavulanic acid (as potassium clavulanate). Over the years, the ratio of amoxicillin to clavulanate has been varied to reflect prescribing needs, to improve convenience and as a response to recommendations for the treatment of more severe infections or those caused by resistant organisms. To reflect local standard amoxicillin dosages, a 500/125 mg (4:1) three times daily amoxicillin/clavulanate regimen was registered in continental Europe (first in Germany, in 1982) and the USA (in 1986). In order to treat more severe disease, 875/125 mg three times daily (Spain and Italy) or 1000/125 mg (8:1) three times daily (France) adult regimens were introduced.

Twice daily formulations of 500/125 mg and 875/125 mg are now available in many countries, and offer increased convenience and patient compliance over the three times daily regimens, along with efficacy comparable to the 250/125 mg three times daily or 500/125 mg three times daily formulations, respectively.32 The adult 875/125 mg (7:1) twice daily formulation was launched in the USA

and other countries from the mid-1990s.

Interesting question.

The key information is in PK/PD model for this drug (drug action). This is fine example, how to taste a knowledge in pharmacokinetics and PK/PD modelling.

Optimal action is the lenght in TIME WHEN the concentracion of drug is over MIC not Cmax! as is seen in ciprofloxacin.

Therefore it is important that there is more than 40 % of time drug concentration OVER cMIC and If the patients take it twice daily there is optimal lenght of time over cMIC. If the patients will take just once daily this time would be only 4 hours, but You need 10 hours or more for example.

If You will take three times daily there are no extra benefit (compare to twice), because time over cMIC is already enough time OVER cMIC.

Regards,

Mathew