Note that this information relates to OUTGOING mail, not INCOMING mail: the latter can usually be collected via any connection to the Internet.
When you send mail, it is initially sent to a mail (SMTP) server provided by your Internet Service Provider (ISP).
This will normally accept the mail, queue it, and in due course (often only a few seconds later) pass it on to the mail machine on the Internet which accepts mail for that address. If there are temporary problems with the delivery, the mail will be re-queued and re-sent.
The accepting machine may either deliver the mail direct to the recipient (if they have a permanent connection to the Internet) or pass the mail on to a storage area, from which the recipient will collect it when they next connect to the Internet and request new mail.
Normally you can only use the mail relay provided by an ISP when connected through that ISP - this is in order that the ISP knows the identity of the sender (from the details given by you when you signed up) in the event of problems with the mail, usually legal problems such as libel, defamation or harrassment, or problems with the sending of messages to a large number of addresses (SPAM). Although logs are kept by ISPs of mail sent via their relays, they are only occasionally referred to, when such problems arise.
If you are able to connect via two or more ISPs (eg, at home or work, or when visiting someone else, or via a public wifi connection), you must use the mail server of the ISP via whom you are connected.
It is possible to configure MailCOPA to cycle through each of the configured mail servers in turn until one accepts the mail. However, this will happen with each message, introducing a delay for each, and could result in a long time online.
Another way round this is if you have authenticated access to a SMTP server, perhaps provided by your ISP or a hosting company. You will normally be able to connect to this via any ISP. Outgoing mail servers can be configured in MailCOPA to use authentication if it is required.
Another possible problem is that a mail relay will only accept mail from certain addresses, eg you cannot send mail from firstname.lastname@example.org but mail from email@example.com till be accepted. Each email address configured in MailCOPA can be set to use a specific outgoing mail server if you wish.
Yet another possible problem is that some ISPs transparently route outgoing mail to their own server, regardless of the one the user wishes to use. This is actually useful as you can specify any mail server you wish, confident you will not be rejected.
Also, some ISPs block access to port 25 (the usual port for sending mail), but some mail relays accept mail to an alternative port, and this can be configured into each outgoing mail server if necessary.