My guess is that oxygen was introduced into the system whan water level and flow rate dropped, and remains even though adding water back to initial level, the added flow rate has not been enough to flush the oxygen out.  Similar conditions of air entry into culverts and water distribution systems can cause changes in water delivery rates that appear difficult to explain.  You may also want to measure barometric pressure and temperature of liquid water changes over time as possible items to consider, correct for.  

You may try to improve the experimental reproducibility, by adequately controlling influential variables; such as the water level, its temperature, and also the air temperature and relative humidity. Barometric pressure may also play a role. A strict cleaning protocol may help to improve reproducibility ― possibly by avoiding surfactant contamination. The water composition should be well characterized and maintained stable. Mechanical vibrations and air currents should be avoided. The observation time may have to be expanded. 

The signalled papers may offer some guidance to properly understand and observe such a system, which is notoriously analogous to a typical dripping faucet system, well-known for its nonlinear dynamics: http://www.nature.com/news/2000/001222/full/news001228-2.html

http://iopscience.iop.org/article/10.1088/0143-0807/10/2/005/meta

Article Chaotic Rhythms of a Dripping Faucet

I think this related to viscosity of the water. Nearly the same method is used to measure the relative viscosity of liquids. Temperature indeed the main effective parameter, as previous colleagues mentioned. You can search the parameters affect the viscosity.

I'd like to add that the variables mentioned by William, Carlos and Sadeq may affect your experiment through changes in surface tension and wettability. If you are trying to get a constant rate under a variable fluid level, I'd would like to recommend trying using a Mariotte's bottle?

I would personally be VERY surprised if you observed that such huge differences in flow rates come from variations in external parameters like temperature or hygrometry. We are talking a 4 to 5-fold decrease in flow rate here. This cannot be due only to changes in viscosity or surface tension.

Before going overboard with a multi-parametric analysis, do a simple test: leave everything as is (including the water in the tank), but change the flexible pipe that drains the water. Chances are that there is some obstruction there, and nothing more. It can be an unexpected debris, a gas bubble, or even simply calcite deposited by water itself on the inner walls of the drain.

If calcite is the source of the problem, then you will have to either use demineralised water, or to install a device in the tank to capture calcium ions from the water.

Hope this helps.

I agree with  the comments  of Carles. Changes in viscosity  or surface tension coefficients due to temperature or pressure changes cannot account for such large variations. However, as your drops are exposed to evaporation, temperature and relative humidity may be relevant if they are highly variable.  But, as Carles wrote, a small gas bubble or deposit of calcite, or even bacterial contamination could have such effects. At these small discharges you should use demineralised and sterilised water, shroud the apparatus to eliminate draughts, and, ideally, keep air temperature and humidity constant.

Dear De Silva, I'm confident of speaking also on behalf of the Others: let us know your advancements!! Regards, giacomo

I think the speed you saw at the beginning was more the outlier to what you are seeing now.

Was the tube filled with liquid or air at the start?

What is the diameter of the tube?

If the tube is a capillary, do you have enough pressure to overcome capillary effects?