In addition to what Nigel says, there is also the likelihood it is a thermal fault, with a component that develops a fault when it's warmed up (most likely a semiconductor), or a soldered or other type of connection which changes from low to high resistance as it warms up (which tbh is unlikely, but easily remedied by re-work).
Just because the picture is going off doesn't necessarily mean the tube supplies are failing. It could equally indicate the video signal is failing or that the low voltage supply to the tube supplies is failing, or something else entirely.
The service manual you linked to looks pretty comprehensive, you should have the information there to check some voltages and narrow down the fault after it occurs. If you can get a solid indication of what area is being affected using this method, folks here may be able to help narrow it down further.
If you don't have the necessary fault-finding skills, your friends here are likely to be a source of hot or cold air, such as a hair dryer, and a source of cold, such as freezer spray. With these you can manipulate the temperature of individual areas and components until you find where the fault is being triggered. Don't use freezer spray until you are 90% sure which component is actually faulty, it's expensive stuff!