First, if you don't know how to release a stuck tool from spindle, tap holder with a with mallet or piece of Brass, then press Tool Release Button while holding Tool holder. If it don't pop, then try holding holder, pressing Release button and tapping...if you don't have three hands...find someone to help.
Make sure Spindle is perfectly clean, no marks, depressions, impressions etc. Clean if you do. Tool holder, the same thing.
Is it one holder in particular giving you a problem? If so, maybe toss..or just don't use. Once in a blue moon we find one that is problematic...
A little oil in spindle, surface, on stud area...clean till spotless.
All that fails...check and clean your filter, that white element gets clogged from time to time.
With front cover off, right over the head casting, in front of Spindle motor is your Tool Release Plunger. It is the Big block of steel with air lines coming into a valve and a pair of Limit Switches. If there is a Stone Exhaust Element, you can try to remove and clean...give a try with removed...just for sh$ts and giggles.
If that don't work...it may be time to look into the Tool Release Plunger itself. Haas sells a rebuild kit for it. It is just a simple Air Piston (Hammer) that uses compressed air to push Ram down with a good Knock... the O-rings wear and the plunger looses its Ummph.
That should keep you busy for a little while.
If your Haas HFO is anything like mine...give them a call and let them walk you thru the diagnosis and fix. You may have something different...or I may have missed something. I like dealing with a skilled tech who systematically progresses thru a fix...they know where I am and what has been done. It's a huge reason I buy Haas.