'Two' plus the adverbial '-s' respelled with 'c' — English built once/twice/thrice, then stopped at three.
From Middle English 'twies,' from Old English 'twīges, twīwa,' formed from 'twīga' (twice, doubly) with the adverbial genitive suffix '-es.' The base is Old English 'twā' (two), from Proto-Germanic *twō, from PIE *dwóh₁ (two). The spelling changed from 'twies' to 'twice' in the 15th century (like 'once' from 'ones') to preserve the /s/ sound. The pattern 'once, twice, thrice' is a complete set — no '-ice' form exists for four or higher. Key
'Twice' is 'two' + the adverbial genitive '-s,' respelled with 'c' like 'once.' English completed the set with 'thrice' (three-s) but stopped there — there is no 'fourice' or 'fivice.' German and Dutch, by contrast, use a productive 'number + mal/maal' (times) system: einmal, zweimal, dreimal, viermal. English chose a unique suffix for 1-3 and then gave up, switching to the analytic 'four times, five times.'