If its a 1/4" bit then yes but on a 1/8" they are often to light and a slight pull is needed.
-Alex
Slight pull while tapping does the trick for me. It’s a lot easier (and safer, I cut myself once while removing a bit) than simply pulling.
I’m glad I read this thread 
Hope this helps somebody. Tappy Tappy.
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For the 1/8" collets, I just ran across them @ sienci.com
Best price I’ve seen on them so far, I believe they’re in Canada so shipping here in the USA might be a bit more expensive than a US seller…but those are few & far between.
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That’s great, Tappity-Tap-Tap… but for me, it’s not the bit that sticks, but rather the collet. Tapping does not let the collet come out.
Sometimes an upward tap on the bit will work. (not with metal)
Hmmmm, I will design my routers, (when I reincarnate) and have my own tool company, I’ll equip all routers with a handy-dandy collet ejector. 
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Mine is sticky too - both the Elaire and the stock. Never had that problem with my previous router. Regardless, a little tap usually breaks it free.
-Tom
So actually tap the collet nut?
I give the collet nut a little tap with the smaller collet wrench if the bit gets stuck.
Most times only a slight tap is all that’s needed, no need for the BFH in this case
Thank you,
That was a $30 lesson,if you know what I mean.