I had a plumber replace my T & P valve on a 08' 50gal. American water heater. It kept discharging water practically every other day. He replaced the T & P valve and water started relieving again 2 hours after the plumber left. Not much, but enough to indicate a problem still exists. What other troubleshooting solution is there, short of replacing the water heater. Should I just replace my water heater?
There are four reasons a temperature and pressure valve will release water.
The valve was physically opened
If you; or somebody else, opens the valve, it will obviously release water.
Since you didn't mention holding the valve open, I'll assume that's not the problem.
If the valve is bad, or junk is stuck in it, it can cause water to be released.
Since a plumber just replaced it, I'd guess this is not the problem either.
Pressure is too high
When water is heated, it expands. This expanding water increases the pressure in the closed plumbing system. If the pressure gets to high, the valve will open to release some of the pressure.
You'll have to put a gauge on the system to determine if this is the problem.
Temperature too high
If the temperature of the water in the tank gets too hot, the valve will open to release some of the overheated water.
Again, you'll have to put a gauge on the tank to find out if this is the problem.
Since it sounds like it's only a small about of water, I'd lean towards high pressure.
To verify this, you'll want to connect a pressure gauge that can remember the maximum reading to the system. Then use the system as normal, checking the gauge from time to time.
Once you determine tha actual cause, then you can start looking for a cure.