I seem to be noticing that the beers I drink early on from my kegs taste less bitter than the last few beers. My kegs do not move for 1 to 2 months while they are being emptied. Is it possible that the hop oils are separating to the top during this time causing the last few beers to be more bitter?
Typically, the Hop bitterness in beer lessens over time. So, you should expect the first taste of the beer to be more bitter than the last drop.
Last couple pints can be more bitter if the beer had micro hop particles that settled out.
Edit: If your beer gets hazy towards the end and increases in bitterness. You have a concentration of matter that CAN increase bitterness. This can be avoided with better fining of the beer before kegging.
My version of the events is that beer wasn't completely fermented initially, and those residual sugars initially masked bitterness, which, as sugars get fermented, becomes more prominent. In keg setup the effect of that later fermentation may not be as visible, but I sometimes notice it with bottles (even when I bottle after I reach calculated FG and check FG readings over a week or so).