Welcome to the wonderful world of OTA DTV!! Sorry, but I just had to say that.
In an apartment environment, it would be very tough to completely eliminate such break ups - or worse - complete freezes and drop out of signal.
That said, the building's antenna and signal distribution system may be part of the problem. There likely is an amplified distribution system that feeds all 22 units.
Adding additional amplification between your wall jack and the converter box would amplify both the signal and the noise up to that point. So going that route is "iffy", and can cost real money.
If you are lucky enough to have a window that faces the direction of the local TV transmitter sites, you *could* try using your own indoor antenna placed near that window. Odds are, you may still have problems, although you may be able to place it to get one or two stations flawlessly.
One thing that may not make a big improvement, but is worth trying, is to use a higher quality coaxial cable (decent RG-6) between wall and converter and keep it (nearly) as short as possible. A long cable just weakens the signal. Cheap coaxial cables with poor shielding (some RG-59's), can work against you, too. Don't use ones with push on connectors. Screw the F-59 connectors down tightly.
I'm referring to the cable from the wall to the converter. You're using S-video, so that's the only coax cable in your case.
The Apex has a signal strength indicator. What does it show on your best and worst channels?