Should I replace a GFI in my kitchen that will not reset?
Assuming you mean you can't reset the GFI even when nothing is plugged into it: Yes, they can wear out and may need to be replaced. Obviously, turn off the power at the circuit breaker before removing this one and installing the replacement.

If you can reset it with nothing plugged in, then the problem is probably the appliance rather than the GFI. Get it repaired or get a replacement.