Welcome to WebmasterWorld Guest from 188.8.131.52
Just my two cents..
I had an incident back to a year ago when one of my sites had a PR6 instead of its actual PR5. When I searched for my site backlinks I found most of the links link to another website that was down for a long period and has an IP on the same class C block of my website. When the other website was up again, mine went back to its PR5. This maybe a temporary fault in Google, but it gave me the feeling that backlinks (and accordingly PR) has a direct relation with IPs.
This sounds more like a shared IP situation. If that is so you should get a dedicated IP address.
I suggest that you do NOT shut down the older hosting package until 15 or more days have passed from the transfer date to your new hosting provider. It will probably help Google to keep all of your pages in the index for sure.