The record for games unbeaten is seemingly 16, back in 86/87, between October and January.
Lost October 4th, 3-0 at home to Stranraer, then 16 games (10 wins, 6 draws) until a 4-3 defeat away to Cowdenbeath on February 3rd.
Just seen you were on about top flight, I imagine you'd have to go season by season as it won't be highlighted in any record book. Vague memory of a decent unbeaten run under McIness but that was maybe just a home record?
Lomas' best run was 7, Wright went 8 in 14/15, between 25th October and 27th December. Can't see anything higher than 8 since we came back up, anything before that is for those older and more knowledgeable than me to figure out.