It looks like your account runs from a jailed shell, I wonder if that might be causing it some how. At least for piping, not sure why that would affect POP/IMAP.
I just created this tutorial on testing piping, see https://docs.blesta.com/display/user/Support+Manager#SupportManager-TestingPiping
This will help you to try piping a sample email from a text file into Blesta via SSH. It should help narrow down the issue.