EMB-145 Captain reported that flight departed with one pack on MEL and during cruise climb the second pack failed. The flight crew reset the failed pack and continued to destination at a lower altitude.

Narrative

(Prior to the flight we had an MEL. Reviewed it. Then the other pack failed while at the gate. At which time we called maintenance and got it working again. I informed the FA (Flight Attendant) that we would be departing and advised in the unlikely event of it failing inflight to be ready for a phone call and prep the FAM (Flight Attendant Manual) in case we needed to talk to passengers and not be caught off guard.) While operating under MEL 21-XX-X for PACK 2; climbing out of FL230 we got an additional indication on the EICAS of PACK 1 VLV CLOSED. The cabin began to climb at a rate of about 1600fpm to which we immediately initiated and requested a descent to 10;000 ft while we ran checklists. The flight attendant was also advised at this time to stop service and be seated to await a further update. We tried resetting the PACK and it responded by turning on which kept the cabin pressure stable while we descended. The highest cabin altitude that was reached was around 4000ft. This was only a precautionary descent; but we both pulled crew oxygen masks in case the PACK failed again and an emergency descent would become necessary. We both agreed that even though the PACK was running again it would be safest to continue to ZZZ at 10;000ft. Dispatch ran fuel numbers which showed us landing with about 3000lbs of fuel. We both felt comfortable with this number and continued to ZZZ at 10;000ft without remark. Ice and terrain were not going to be an issue and it was severe clear even though it was night.The other pack failing at gate and still continuing to proceed with flight instead of figuring out root cause.Knowing we had an issue at the gate; with the additional pack; advise less experienced captains to add into their brief about prepping the FA and FO (First Officer) on proper procedures as to not be caught off guard. Be ready to recognize the signs. And put a little extra fuel onboard as standard practice in case of the 2 pack failure with Dispatch.