Slow authentication?

Let's say I have a local domain controller for domain A in (for expediency
sake, say, New York). If I am already authenticated (through this DC), and I
try to access a network resource (which is also in domain A) should I not be
re-authenticated? Shouldn't I already have a "ticket" that let's me access
the resource instead of re-authenticating me?
We are having issues where after logging in (to the network) users are
mapped to a file share (which exists on the same domain), but first access to
this share is extremely slow. I'm wondering if the users are being
re-authenticated or it's something else.
Any help in this direction would be much appreciated. Thanks
.