Question About Tippet

I took this sport up in October of last year, so I'm still a novice -
pardon me if this is a stupid question,

Last week, I broke off my 7x tippet at least 4 times on strikes. It
broke anywhere from just below the knot joining it to the leader, at
the hook, and other places in between. This happened with two
different spools and types (Orvis and Frog Hair) 7x. None of the
tippet is old (according to the expiration dates, at least). The last
few times I broke off, I replaced the entire tippet - but it still
broke off. (Oddly enough, I don't break off once the hook is set.)

I haven't had the same problem with 6x, which leads me to believe I'm
doing something wrong. I'm still catching fish, but would prefer for
environmental/stealth reasons to go with the lighter tippet. I'm
careful in handling the tippet, and am using a surgeon's knot to
attach it to my leader.

Can anyone hazard a guess as to the flaw in my technique that might be
causing me to break off with the 7x?

And, if you catch an obstruction (tree on the backcast, underwater
rock/ log) but manage to get off. Is there a method for examining the
tippet for damage, or should it usually be replaced as a precaution?

I'm going to ask down at the FLFS (friendly local fly shop) also, but
hoped someone here might be able to shed some light on it.

TIA-
Charles