As with almost all computing-centric issues, there are many possible reasons for this.
The first thing to check is any bounce-back error messages, as they often contain a description of the issue.
It's also worth testing sending mail directly from the address you're forwarding through by setting up a mailbox for that address.
The reason for this is that some receiving mail providers such as AOL, and BT often reject/delay the receipt of forwarded mail as part of their filtering process.
Sending mail directly from a mailbox rather than forwarding the message should make apparent whether or not this is the case.
If this is the case, it is likely to be down to a spam policy they enforce where their spam filtering system assumes that mail claiming to be from a different address to the one it's actually from (i.e. the address it was forwarded through) is not legitimate, and, as such shouldn't be allowed from external servers.
This means that their policies prevent the forwarding of messages, and so in these instances forwarding is not possible.
While we'd love to persuade these companies to change their policies, they are generally quite keen to stick to them!
You can though maximise your chances of getting these messages delivered by setting up an SPF record on your domain, which validates the authenticity of the servers you specify in the record, meaning they're validated, and less likely to be seen as spam serving servers.