Chiming in ....
Coupling caps usually keep there leakage once started, but agree on replacing at least the coupling caps.
But what might also have happened was that cathode bias was temporarily lost because of a shorted cathode bypass capacitor for the power stages. Judging from the SX-34 schematic (could also not find an Allied one), they have a common cathode resistor for all 4 power pentodes bypassed by a 50µF 25V electrolytic (C35 in that schematic). Such a cap may have shorted and then 'burnt out', restoring the resistance. I would suggest at least replacing that as well; visual inspection might be revealing. This particularly so if said cap was mounted close to the very hot cathode resistor (electrolytics and heat do not go together very well).
Also guessing (the route I would follow) is suspicion of resistors R51 - R54, again as per the SX-34 schematic. These values are quite high for grid stoppers; might also have failed temporary because of age. But I would first examine the cathode bias stuff - a little suspicious that all four coupling caps would start leaking at the same time, and then again self-heal at the same moment somewhat later ....
(And while busy, you said it was an old set. Tube holders etc, have a habit of becoming oxidised/rusty after time. Some attention thataway may not be in vain.)
But as asked before, kindly do keep us informed! Someone else's experience very informative!