[exim] Forwarding messages from gmail

Is there any history with problems with gmail, in particular, with
forwarding?

Heres' the problem I'm having. My host provider uses Exim. My domain is
angelhostel.com My host provider is penguin hosting.
My most important email address, obviously is reservations@???
Using the cpanel, I've set up forwarding to my own personal email
alex.miller.boston@???

When I send an email FROM alex.miller.boston@??? to
reservations@??? the email gets destroyed. The host provider
says that it's nothing they are doing. When I send an email from some other
source than gmail, like hotmail, it works.

When I turn off forwarding, I am able to receive emails directly to the
reservations@??? account but only when forwarding is on does the
emails from gmail disappear.

Any history of this? Obviously gmail is an important and common sender.

Alex