SourceTree losing SSH key / configuration after period of time

I have SourceTree setup to use the OpenSSH client, which prompts me for the password for my SSH key at startup. This works fine for most of the day, howevever sometimes I'll find that push/pull operations no longer work. The progress bar just spins in its indeterminate state forever. This occurs pretty much every day when I get into work in the morning, as if it's losing the SSH agent connection after a period of inactivity. I can fix this by restarting SourceTree but have not found any other solution yet.

I keep SourceTree open on my machine pretty much constantly, my machine is left running all of the time too, only ever rebooting for updates.