Thanks fellows. It was really a time consuming process to track down the problem, since I only had a 2-minute time window per hour to measure stuff. Beyond that time window, everything was normal and I couldn't do much.
Long story short, it turned out that the pin 1 of U650 (display sequencer module) was broken and had a flaky contact. As a result, the selector signals sent to U800 was incorrect. It forced U800 to only output the readout signal, instead of switching between readout and sweeps.
As for why the scope functioned normally after a few minutes, my guess is that the broken pin expanded with accumulated heat, and the flaky contact became "solid" when the scoped was warmed up.
With the broken pin fixed, I tried a couple of cool-off-and-then-power-on testings. The scope no longer showed the symptoms described in my original post. Problem fixed!!
A few notes about U800:
I heard a lot about how easily it could be fried when running with an open case. So I checked its temperature with my finger tip frequently when poking around (I don't have a service fan). Interestingly, the U800 in my scope did not heat up quickly. It only felt warm after running 10 minutes without the case.
YMMV, though. It's hard and expensive to get a replacement. Be careful and play safe!