Our organization is using Mail by Google in a testing phase pending full blown rollout. Beginning after close of business yesterday, we began noticing the problem mentioned in this thread, i.e. "Network Unavailable" messages when trying to retrieve messages. The same problem is currently happening, though intermittently, with the regular Blackberry GMail and GTalk clients.
In addition to this, we have noticed a problem loading https pages in our Blackberry browsers. We are unsure whether this is a Google problem or a RIM issue, but would appreciate any additional information.
I invite you to visit and post related comments to the following Google forum: Mail by Google Blackberry App not connecting - News & Updates | Google Groups