The Hypcons are sensitive to being clean and the contacts being aligned right. You should remove each and clean the contacts on the chip and connector. Also do this to the other ICs and transistors. The square mounting frames for the Hypcons should be put on with an even pressure on all sides. The screws are tightened to snug in opposite corners at a time as the lug nuts on the wheel of a vehicle. I did add good heatsink compound to the Hypcons and the heatsinks. Roger is right about making sure the coax connectors are also cleaned. It is possible the neck pins have oxidation on them. Check the voltage at the input of the vertical if cleaning does not fix the problem. It is possible the problem is earlier. One dirty contact somewhere can cause headaches in finding it. Many here will agree to this having seen it enough times.
IF yours looses sync in the readout, the 741 IC under the handle on the horiz. board towards the rear will be bad. I had this happen in mine. It will occur when it warms a little. This happened in mine after a minute with the left side off. The trace will remain normal. This information is only in case this happens to yours or anyone else's.
Jon is right about keeping the intensity low. When I use mine, the intensity is enough to see the line and readout. When a trace is on the screen, I turn the intensities up a little. The intensities I keep it at are so that it is barely visible until I raise it enough to see a trace and readout which is still low. The yellow LED will not come on the way I keep the two set. It may be easier to use a lamp on the circuit while keeping the screen in a low light level to ensure the trace seen is safe for the MCP.