Ok, it will keep running when jumpered. Did you jumper and leave running for awhile ?
Set t-stat for how you normally do and jumper it is what I was meaning.
IF it never cycled again on and off, it was a bad fan switch. IF it was something else, it should have still cycled on and off.
Since you replaced it and it is still doing it, test across the upper limit with manual reset.
With unit running fine, it should read 0vac across the terminals.
When the unit blower cycl;es off, if it gives a reading suddenly and has to be reset again, it could have become weak also.
Some people are Humbly Grateful, while some are Grumbly Hateful.................... Which one are you ?