With proper care, there is not really a limit. Orchids grow and replace old growth with new perpetually. As long as they don't get a virus or other terminal illness they will keep going.
I have plants purchased as adults 30 years ago, they likely were at least 10 years old when purchased. I have have heard of 100+ year old orchids in conservatories.
There are some short life-spans among certain very small or terrestrial orchids, but the most commonly grown Phals, Paphs, Catts, Vandas, Oncids etc. can all easily outlive you.