Just because your mentor is an expert in somethings, don't assume she knows everything and everyone. As mentoring is supposed to be active on both sides of the relationship, here's a few things you can do to help.
1 - Don't assume your mentor has already combed their network for the right connection for you and your current questions.
Always ask your mentor "Who else could I talk to about this?"
On the flip side - don't be afraid to offer your mentor new people with whom they can connect. We don't know everyone in the world... yet...
2 - Don't assume your mentor is an encyclopedia.
Always ask your mentor "What associations/groups/websites might be worth exploring on this topic?" Don't assume your mentor will hand you everything in one neat package.
On the flip side - bring your mentor good sources you find! We're always looking for fresh insight too.
3 - Don't assume your mentor's network is boundless.
Invite your mentor to explore some of the events and meet new people with you.
On the flip side - make sure you've investigated the sources your mentor has offered you before suggesting exploring the unknown.
4 - Don't assume your mentor is a strong networker.
It's a difficult skill at the best of times. I am the consummate "reluctant networker" and people come to me for advice!
It seems to be an assumption that with mentoring comes networking and invitation to new folks. But, sometimes, the focus is on a one on one discussion of the subject matter only.
Discuss your questions around networking and ask for advice... but on the flip side... ask your mentor what their challenges and hesitations have been and how they've been overcome (or not).