Unusual problem with Swoop on Mac OS 9.0.4 under SheepSaver
Sorry it's taken me a while to respond, but as promised in the comments I've tried to replicate this problem at my end.

The good news is that I could in fact replicate the problem. The problem occurs on five separate SheepSaver installations on three different Macs (running Tiger, Snow Leopard and El Capitan). I've tried various preference settings, along with experimenting with Mac OS 8.6 and Mac OS 9.0.4 installations. I've also tried booting SheepSaver with extensions off, and tried playing Swoop without sound.

Long story short, I couldn't play more than two consecutive games before SheepSaver froze.

As a final check, I tested Swoop on a standalone 2002 Quicksilver PowerMac G4 running Mac OS 9.2.2. Swoop plays flawlessly! :)

So, in a nutshell, I know this isn't the answer you were looking for, but I don't think you're going to get Swoop to work properly in SheepSaver. You could try some other emulation software, such as Basilisk, or purchase an older Mac capable of booting directly into Mac OS 9 (or running the Classic environment under Mac OS X). If you happen to want to try the Classic environment, post a comment and I'll happily test this for you (I have a couple of Macs that can run Classic OS under OS X).

Either way, good luck!