A proposal for lunar development, LunarCOTS, relies on a reusable shuttle running on LH2 and LOX to work. It lands, is refueled on the lunar surface, and then takes off again. Presumably it could sit for days between firings, and would fire many times over the course of months or years. I'm working on adapting that mission architecture, and this part makes me more nervous than usual.
I know the J2s on the Saturn 3rd stages restarted once up to 6 hours after shutting down during Apollo missions. Have liquid hydrogen engines been restarted more extensively since then? Is this a big technical challenge?