IMO the best way to do this is to spend some time doing (or finding and studying) a technical analysis of the progression - understand how it works theoretically and make into an abstraction: Simple examples:
- This tune is a I-IV-V blues in G.
- This tune is a sequence of II-V-I's that move through every flat key and then
a turnaround back to F.
- This tune based on Rhythm Changes in Bb.
By learning a piece's algorithm - an abstraction of the specifics - you no longer have to concern yourself with the details of each chord: You know the formula - you just have to follow that. By doing so, you will be able to quickly learn even fairly complex pieces and remember them, because you aren't getting bogged down in specifics.
Another way of saying that: You need to understand the music you have to play, not just play it by rote.
This is a tried and true method in any discipline that requires one to have large quantities of complex material ready for use at any time: Generalization and abstraction are the key to acquiring and maintaining large stores of information in your mind.
Another way (if it's possible in your situation) is to make yourself a cheat-sheet: a very concise chart that you keep in front of you somehow -
maybe even taped to your wrist or your instrument somewhere that you can see it - for the parts that you have to play and have difficulty with, and look a little ahead at your cheat-sheet when you're coming to the tough parts. Of course initially you're not keeping track in your head that way, but by doing so you should soon have the changes imprinted in your brain.
This is quicker and easier method than the first one, but is less effective and beneficial in the long run. Once you learn how to analyze and abstract a tune, it's a skill that will move you ahead no matter what sort of music or musical endeavor you're involved with.