GFCI problems can be tricky to track down and it may take several trials and errors, until the problem is resolved.
If it ran for awhile with the elements on, it may be a circuit overload. Did you check to see if there are any other appliances on that circuit that may be causing an overload.
When you plug it into another socket make sure it is not on the same circuit this GFCI is connected to. Try plugging the P10 into a circuit that has an outlet that is controlled by a different GFCI. If it works on a circuit that is controlled by a different GFCI, then the other GFCI needs to be replaced. These sockets can go bad.
A power strip, especially ones with a surge protector can sometimes be the cause. If you are using a power strip, don't use it, and plug the P10 directly with an extension cord.