How could mIRC (or any other IRC client) do this? To get "offline messages", someone has to log them while you're offline.
The logging has to be done either by another "client connection" to the IRC network, e.g. listening for messages containing your nickname (for example a
bot you set up and host remotely), or by a
bouncer (a remotely hosted relay connection that keeps "your" connection alive) with a "log feature".
Or the network itself stores messages for you - some network feature a
"MemoServ", which other chatters may use to leave a limited number of notes for "you" (your registered nickname). That's a network feature, of
some networks, and in no way related to mIRC.
Anything beyond that would make up a (theroretical) feature request for the developers of the different
IRCDs, which are developed 100% independent of the client software you use to connect/chat on an IRC network (like mIRC). And it's very unlikely to happen ever, for the way the
IRC protocol is designed. Many networks / IRCDs don't even support nick registrations - and to identify to "your messages", you'd need a
standardized account system etc pp. Keep in mind that IRC is more than mIRC - it's a protocol, used by dozens of different chat clients on dozens of different IRCDs, and designed for
online chat.
On a general scale, the constrainment of developement of any features like your request is not caused on the client side. It is caused by the heterogeneous IRC "networkscape" which had evolved over the time - by the fact that there's not "the one" IRCD. Have for example a look at the
IRC+ project ...
