Here are the prospected F1 teams that failed for F1 entry for some reasons:
Prodrive in 2008, 2009, 2010 and 2011 - because of attempting for using McLaren customer chassis but vetoed by Williams due to ban of F1 customer cars.
USF1 in 2010 - because of lack of funding, sponsorship as well as resources.
Forza Rossa in 2016 - because of omission of F1 entry registration.
any additions?