That rules out my initial line of thinking about what the source of the problem might be. The only other thing I can think of is if this might somehow be related to security software (e.g. a firewall that needs to be 'primed' before allowing the connection). Would you please restart your computer in Safe Mode (with Networking), fire up GSAK, and see if GetMail works the first time? If it does work in Safe Mode (with networking) it suggests some other software is interfering.
If not, we'll need Clyde to weigh in on this one.
If not, we'll need Clyde to weigh in on this one.