I think he was making an implication about the typical infrastructure you'd expect to have surrounding an Eggdrop versus a client-side mIRC install on a desktop PC.
A desktop runs at home, where the machine could be shut down, where other things happen on the same machine, where the internet connection is only *fairly* stable and where electricity might cut out.
An eggdrop *typically* runs on a shell which is *typically* located in a server farm inside a data center somewhere. In a place like that, the machine is likely not to be used for anything else, has redundant connections and power and will never be accidentally shutdown by anyone or anything.
In that sense, an eggdrop-- or frankly, a shell account with any IRC bot, is more stable than running mIRC at home. And of course, an eggdrop running on your home desktop PC is going to be no more reliable than just running mIRC.