Can I reconnect to a computer if my reservation time has not expired but I disconnected?

Yes. Just run Remote Desktop Connection or SSH again and login with the same user name and password. You will have 15 minutes to reconnect, before your reservation is timed out.

Reconnecting to a Remote Desktop session on a Windows server will show you to the "desktop" you were already using, with all of the programs and files you had open. Whereas reconnecting to a SSH session on a UNIX or Linux server will be like logging in initially, any programs you had running previously will no longer be running.