Why is absorbance at 280 nm for protein solution going up when I measure repeatedly?
It looks like your protein concentrations are right on the limit of detection of the spectrophotometer, and changing the diluent buffer changed their concentrations. The samples may not have been thoroughly mixed after dilution and before measurement, so the varying measurements may simply be the solution coming to equilibrium. Temperature can also affect absorbance, so you should verify that your samples have equilibrated before drawing any conclusions. If the absorbance of your phosphate buffer is 0.03, I'd try to keep the sample absorbances above 0.075 or higher to avoid getting too close to the limit of detection. Also, make sure your buffer isn't too old or contaminated with something which could be affecting its absorbance characteristics.

I would suggest taking one or two protein samples and doing a dilution series (1:1, 1:5, 1:10, 1:20) in a large-ish volume (say 400 ul each, if you can spare it), vortex briefly to mix well, then measure triplicates of each dilution on your reader, along with appropriate blanks (buffer only). You will see differences between each measurement, but it should be quite small, depending on the accuracy and precision of your instrument. 

Measured values will not be exactly the same from measurement to measurement, and it would take a lot more than three repetitions to determine if there was an actual drift trend occurring. Measure your sample plate every 5 minutes for an hour and plot the values (don't just eyeball them) to see if the machine may need to be serviced.