Sounds like your team / formation are set out to win games early on maybe your doing too much too soon and players are getting physically and mentally tired in games causing complacency and allowing teams to nick a goal late in the game?
Sounds like the game is easy if so many people go unbeaten for long lengths of time, im currently 23 games unbeaten with Hartlepool in my first season also.
Started a game unemployed and Derby County came knocking.
One of my favourite games to date, started bottom of the league when I took over and got them promoted from the Play Offs in the same first season.
Bueno was an absolute force, sadly couldn't afford him in second season so got Wickham...