Air carrier First Officer reported a malfunction of the runway lights while on final approach at night at a non-towered airport. The flight was unable to reactivate the lights then diverted to an alternate airport and landed.

Narrative

During flight ABCD from ZZZ to SCK; we diverted due to runway lighting issues on final approach to Runway 29R.We activated the runway lights approximately five minutes prior to intercepting the localizer; and all lights initially illuminated (HIRL; PAPI; and edge lights). However; at approximately 800 feet the edge lights extinguished while the remaining lights stayed on.We attempted to reactivate the edge lights without success; which led us to execute a missed approach. ATC was advised of the situation and informed us they would attempt to contact airport operations. We then requested vectors to enter the downwind leg for Runway 29R to attempt another reactivation of the runway lights; but this was unsuccessful as well; and we elected to divert to ZZZ1.While on approach into ZZZ1; ATC informed us that flight ABCE was able to land at SCK. However; considering operational safety regarding fuel; we continued with our diversion and landing at ZZZ1.Once on the ground; we heard ATC advising another aircraft that SCK's runway lights had failed again.The aircraft was refueled; after which we proceeded to SCK and subsequently operated flight ABDF to ZZZ2.I remain available for any further clarification.