Cannot Find Transaction IDs in PayPal

I have about a 100 members on my site that uses the Membership plugin. I’ve only just started using this plugin, and now I wonder if this was a mistake. Subscribers have reported to me that they never received a payment notification from PayPal. When I search on their names in my PayPal account there are no results. When I search in PayPal on random transaction IDs – as copied from the ‘view transactions’ in Membership – there are no results either.

Can you tell me what’s going on?

(This is Membership 2.1.4 on a WordPress 3.3.1 site.)