With no cable inserted, the signal flows through a shunt in the jack. The shunt is a switch, the contacts become oxidized with time. This impedes signal flow. When the instrument cable is connected, the shunt is opened, signal now flows out the preamp out jack, through the cable, into the power amp in. This bypassed the shunt connection. If it corrects the issue, the shunt needs to be cleaned. The solution is to partially insert a plug which will open the shunt and apply deoxit to clean the oxidization. This is a maintenance task that most amps require fom time to time.
I presented this test because it is a possibility and easy to test. You have to sweat the details and check out the possibilities. But because the issue goes away after the amp is on for a while, it appears to be a heat related issue. A bad contact is getting better when metal is heated and expands. An easy thing to check is a bad tube or a loose tube socket contact. There are other possibilities that a tech could check out.