Sensitivity to antibiotics in a live animal is more complicated that in vitro sensitivity. In vitro, the antibiotic is essentially applied directly to the bacteria. In vivo, the antibiotic has to reach the bacteria in sufficient concentration to be active, so the pharmacokinetic properties have to be matched to the tissue infected; for mastitis, you would need an antibiotic known to have good levels in the mammary gland and milk. The antibiotic also needs to be active in the conditions where the bacteria live; if the site of infection has an acidic pH and/or low oxygen tension (eg sites of suppurative inflammation and necrosis), the antibiotic has to be able to be active in those conditions. If the bacteria is a facultative intra-cellular organism (eg. salmonella, staph aureus), and the antibiotic used is not sufficiently lipophilic and therefore does not penetrate inside cells, you can have chronic persistance of the infection. 

Organism may be resistant.. 

As a general rule, antibiotic susceptibility tests results are quite reliable. Nevertheless, there are not guidelines stablished (CLSI, EUCAST)  for all microorganisms and antibiotics, and in this case you should "adapt" guidelines estblished for similar microorganisms. Otherwise, when studying discrepancies between in vitro results and clinical results, you shall have in account the antibiotic pharmacokinetics. Though in vitro activity is good, if the antibiotic does not get to infected área at good concentrations , the clinical results will be por.

Sensitivity to antibiotics in a live animal is more complicated that in vitro sensitivity. In vitro, the antibiotic is essentially applied directly to the bacteria. In vivo, the antibiotic has to reach the bacteria in sufficient concentration to be active, so the pharmacokinetic properties have to be matched to the tissue infected; for mastitis, you would need an antibiotic known to have good levels in the mammary gland and milk. The antibiotic also needs to be active in the conditions where the bacteria live; if the site of infection has an acidic pH and/or low oxygen tension (eg sites of suppurative inflammation and necrosis), the antibiotic has to be able to be active in those conditions. If the bacteria is a facultative intra-cellular organism (eg. salmonella, staph aureus), and the antibiotic used is not sufficiently lipophilic and therefore does not penetrate inside cells, you can have chronic persistance of the infection. 

Effect of an antibiotic in a clinical situation often does not match the laboratory results for a number of reasons; some of them are given below

•  While effectiveness of antibiotics is more or less predictable in case of Gram positive organisms, Gram negative bacteria often keep changing their behavior resulting in significant variation in susceptibility pattern in different populations.
• Absorption of antibiotic and penetration at the site are important factors; most antibiotics have poor penetration to meninges, bones, joints and heart valves where higher doses are required.
• Presence of pus or a foreign body at the site of action can also render the antibiotic ineffective. Drug interaction can also play a part.
• Laboratory sensitivity tests have their own fallacy. While many antibiotics exhibit have clinical effect similar to that shown by laboratory tests, others behave differently; quinolones, aminoglycosides and tetracyclines often show misleading results; e.g.,  quinolones often show good sensitivity for Staphylococcus aureus though the latter is almost useless in clinical situations. Moreover, the disc sensitivity, as it is measured by area of inhibition zone, may be fallacious; two agents may appear equally effective while there may be a significant difference in the size of two areas - the laws of geometry are such.

The moral of the story is that though laboratory sensitivity tests are a good guide, they can not be trusted to show the same results clinically and a clinician should be open to all possibilities rather than to blindly follow lab results. 

In vitro antibiotic sensitivity results do not always reflect in clinical outcome. Some of the points are already mentioned by other contributors.

The most interesting aspect is that in vitro resistance is more predictive of treatment failure. Hence if in vitro tests show resistance, the antibiotic should never be used in clinical practice.