My Kirby Superstar cartridge keeps having issues. For one, the smallest push of my console seemingly causes the cartridge to disconnect. Secondly, the save data keeps erasing. I don't know if this is because of a dead battery, because sometimes the save data works, other times it's deleted when I turn on the game again.

Both problems usually happen at the same time, so I'd imagine that the save data erase is tied to the cartridge getting removed during gameplay. However, if that's the case, that's really friggin dumb. It'd make sense if I pull it out while the game is saving, but no, usually the cartridge is removed in the middle of a level.

Is it quicker/easier just to replace the game, or should I fix the cart I already have? How would I go about doing that? I really wanna play this game, I've made multiple attempts, but I don't feel like replaying the same parts all over again.

If I ever dive int an old classic that requires a significant amount of time I always make an effort to replace the battery before moving forward. especially now in games such as those NES/SNES/GAMEBOY since those battery's have had over 20-30+ years to degrade. You will have no choice but to start over.  

as for the game not seating correctly, is it just this game? Have the contacts been cleaned? Is there any noticeable damage to the bottom of the plastic on the cart? Is there anything perhaps small that may have fallen inside of cartridge slot on the SNES?

Get the battery replaced, clean the cartridge and clean the cartridge slot. With a properly cleaned cart slot, SNES games should never freeze from being moved or touched.

If the save is there sometimes I would be leaning more towards the reset IC or the SRAM chip. Still a good idea to replace the battery also.

If you are in the US I could take a look at it if you don't mind sending it in.

Do you have any issues with other games? Possibly a power issue with the AC adapter? You could check the voltage on it if you have a multimeter.

It could also be an issue with the SFX chip in the game, maybe? I'm not an expert on this, though.

Super Star uses the SA-1 not the FX chip.

Both the FX and SA-1 use the SRAM as work RAM, I once fixed a broken Yoshi's Island that was displaying corrupt graphics by replacing the SRAM chip. The SRAM chips in these type of games goes through a lot more wrights than standard SRAM games that only use it for saving.