On the face of it, looks like the biggest mistake during the early 60s was not replacing manager Frank Hill and instead promoting somebody from within for a 2nd spell in charge, Gary Brazil style.
1960/61 losing at home to promotion rivals Grimsby in front of 22,292 probably knocked a lot of belief out of the club, the start of a 6 home game sequence without a win, a run ending with defeat to Bury who were one of the sides to go up. Don Roby then left for Derby at the end of that season and they don't appear to have brought in an adequate replacement, Fry arrives from Newport but only plays 15 games in 61/62 and Brian Moore from Stags who makes 14 apps, Frank Hill possibly sacked prematurely on 31st October (he was the man in charge for the 59/60 promotion), Tim Coleman back into the role and finish 13th.
62/63, Lawton/Sewell era nostalgia apparently kicks in with the club reverting back to white shirts, Astle comes into the picture and starts banging them in alongside Hateley, but that terrible winter creates a backlog of more away games than home in the run-in and they only win one game on the road in the 2nd half of that season, Hateley leaves in the summer, replaced with Terry Bly who scores only 4 goals in 63/64 whilst the other new signing Mike Barber gets an injury that ultimately forces him to retire and under a player/manager Eddie Lowe (age 37) it's relegation back to tier 4. Incredibly they stick with Lowe the following season, which proves to be a then all-time low.