I've been doing mixing remotely for a job for around 5 months now and I've had some major ups, major downs. I was kinda forced into it after being offered a tour I couldn't turn down with my band and losing my day job as a consequence.
I tend to attract clients through my name as a frontman in a band so that's one of my main angles, though recently I've had people just approach me randomly.
My advice is to offer a lot of services. I'll write drums for people, edit drums, write music etc... If you're priced reasonably and your work is good then you have half a chance. You need to undercut the competition, but not price yourself too cheap. So if a mixer starting out charges $80 for a track, charge $80 but offer them the quality of somebody twice the price and move up from there.
I'm really starting to look into expanding my client base which is why I'm on here. Ultimately it's about starting good working relationships with musicians, delivering a result that exceeds their expectations and stops them wanting to go elsewhere. A year or two down the line, they'll come back for another album.
The hardest part is getting started. Getting your initial client base. Contact people, offer them a track mixed for free as long as they advertise you and tag you in it. Things like music videos etc.
It can be done though. I'm determined to prove it over the next few years! lol