I just mess with the slot a lot. I've never known one to stop crop out completely, they just take a while to get working.
I've known them to crap out completely, or take 30+ minutes to get working at which point I give up.
Added in edit: I spent about 15 minutes tinkering with one that has a particularly bad cart slot. I tried the following.
Netlink
First Party Sega Memory Card
Third party Interact Memory Card
Action Replay 4 in 1
I put in each cart 15 times in various levels of how far I put it in, the only cart to get any sort of a read (IE the All rights by Sega Screen pops up before it goes to the main menu) was the third party interact card, and when I went to the memory menu it still couldn't see it.
Further edits:
After a few tests in my Japanese Saturn, the third party, first party card and the netlink were all read within 5 tries. The action replay was not successful. So the problem is the slot, not the carts (well, maybe the action replay).