Have no idea if it allows access to ashMaiSv.exe.
If you can send and receive mail then ashMaiSv.exe is allowed in your firewall.
Why you can send emails you create but can't send replies is something that avast doesn't care about, it doesn't differentiate between replies or sending emails that you create.
This does sound strange, what email program are you using?
Do you have more than one email account that uses a different ISP connection? It may be that it won't allow an email to be sent if the sender isn't logged on to their ISP connection.
What error messages are you getting when you can't send replies?