I've been through this using small compressors for DA sanders.
What I did was to throttle the air down with the valve on the sander. (It actually seemed to sand better at the lower speed.) Then when the speed dropped too low for good sanding, I would stop for a moment to change paper and let the compressor catch up.
I found it was a good idea to not let the pressure come up to the point that the compressor motor stopped, because it was hot enough that it really didn't want to start again.
Also, if possible, don't run the compressor on an extension cord. Having full voltage sure helps.
If it turns out your compressor just isn't up to the task, consider getting a good electric DA sander. Back when I was painting
cars for a hobby, they just weren't available. Now just about every tool outfit has one. From some of the other forums, the Ridgid is probably the best buy, with the Festool the best overall. However, as with anything else, there are a lot of opinions floating around. I happen to have both a Porter Cable and a Festool RO125.
You can also hook your vacuum up to most of the electrics. This is important, since the stuff you are sanding off isn't the nicest stuff to breathe.