Difficulty deleting records

[Clare]

Hi again, another question:

Lately, people have been saying that records they delete reappear later on. These are records that are displaying in a portal, but they are being deleted from their own layout. If the "allow deletion of portal records" box is not ticked, does that prevent them being deleted from within the portal only, of from anywhere?

Again, in the hope of anyone's helpful insights into our woes, I have attached a screen grab of the relationships graph (clone file is too big to upload, even zipped up). I didn't design this database, and am still a learner - so it's proving very hard to go back and figure out problems.

Really grateful for any help!