I wouldn't be worried about the train being cancelled. It is of course possible that there is a crash or other accident that physically blocks trains along that route, or there is an unexpected equipment failure which is not detected until the train is coming out of the depot at 5am, but this is rare.
Long delays are unlikely although short delays of 5-15 minutes are common. Your train has 15 minutes slack at Leipzig and 6 mins at Frankfurt(Main) Main Station so it may be able to catch up on minor delays.
If your train is unexpectedly not running, you would be allowed to take subsequent trains. The next direct service runs 2 hours later and should give you just about enough time to still catch the BA flight; but the DB website also provides an option leaving 1 hour later along the same route, changing at Leipzig and Frankfurt(Main) Main Station, arriving FRA at 1214 which is plenty of time.
I thought that flights from DRS were quite sparse, but having looked at the flight timetables, there are actually 3 flights that would suit you. I would be a bit nervous about taking the 1050-ish flight as there are no alternatives if that is delayed or cancelled, which to me is more likely to happen than the train being delayed significantly or cancelled. But you have already booked the train, and the 0630-ish flight is super-expensive on most dates, you aren't flying LH to the US, and you probably don't want to spend hours at FRA should everything go to plan.
If you have checked bags you will have to go landside and re-check at FRA, and there is a non-zero chance that BA will not let you check in online because it wants its agents to inspect your passport manually for "security". If you were flying LH to the US I suspect you may have chosen the flight from the outset, but in this case I'd stick with the train.