As Zulgh said, there is a check against con, and only con. Save might play into it landing, but once it is on you, you get the hourly check against your con, not your save.

Rot has a good chance to decrease con, but not on people with high con. I'd say if you are an elf, who only has 16 highest, they can save the con checks. Not every time, and the saves will get harder as they lose, but if they have enough ear to keep the checks going against a 16, they probably won't be losing a point every hour, otherwise rot would essentially just kill the elven races. If they wear + con gear, then even when it goes down their next check will still be against that 16 con.

You could rot a dwarf with 25 con, he'll never miss a check for the most part. I would say anyone with 20 con or more does not worry about rot actually killing them, especially if they have a few pieces of gear to boost their con up, which most every hero carries I'd say at least +10 of in a container.

The only thing I do not recall is if your con check goes against your natural or adjusted, but I thought I saw it said once that the check is against natural con. So + gear allows you time to wait out, but does not help it from going down.
But I am not sure about that, an Imm would know best.