Zach is correct in stating that the gear is held down by "over-center". The springs and bungees do help hold the gear over-center. I agree the springs are important. However PA24's flew several years and many hours before Piper mandated the second spring and bungee change intervals. (From the late 1950's until 1977, in the case of the bungees). That said, I have literally seen aircraft brought in where the bungees are laying loose on the inspection plate (just hanging). Not because they were worn out, but because they were incorrectly installed 3 years prior by a different shop. Given correct landing technique and the electric gear system functioning properly, a Comanche can be landed almost innumerable times without the bungees. Mind you, I'm no advocating that, just stating what I've seen. If you read the AD 77-13-21 it states the purpose of the bungee change interval and the bushing wear check is to prevent gear collapse when manual extension is used. The nose gear springs also serve to keep the gear down and work in much the same way as the bungees. The gear system works in concert, the springs (originally a nose gear bungee), the main gear bungees and the motor and transmission all help the gear stay over center and "down and locked". But the important take-home message is this: If you only check one thing on the Comanche gear, BE SURE IT GOES OVER CENTER.
To restate the opinion on how often to change bungees, that is up to the owner. The FAA and Piper Aircraft recommend every 3 years or 500 hours. As an IA, that is good enough for me.