Not likely. The power valve cannot leak the fuel out of the bowl, and the 2GC carb has the needle/seat on the top of the carb, so fuel pump drainback is not an issue. You are suffering from the fuel issue discussed earlier, and the fuel is simply evaporating below the level of the accel pump supply slot. You either live with it, or start the engine more frequently. You can also use an electric pump as suggested above. Verify that your accel pump is, in fact, operating and functional (strong solid squirt when the carb bowl is full). If it is, you have little recourse on this issue.
There is a remote possibility that you could have a cracked or porous carb casting. To verify, you can pull the carb, fill the bowl, and set the carb up on your workbench on top of some tall sockets at the throttle plate bolt holes: Observe the bottom of the carb for leaks or drips. If nothing is dripping out the bottom, your only problem is the evaporation issue.