Wait a minute ... on second thought it may not be the connections (that usually doesn't work by trying it again).

It may be the ignition switch, or maybe the starter -- an auto electrician should be able to diagnose it pretty quickly (if you can get it to happen when it's at the shop ...).

Full power goes through the 1200's ignition switch, so they tend to eventually wear out (most cars use a relay so they last longer). The switch is a round thing behind the key part, it unscrews and a new one is put in.