In terms of the website appearing, theres the issue of downtime, as ithelp has mentioned...but also the chance of the server not supporting scripts that you would like to use, and having a nightmare trying to get them added.
Also, theres the problem of how you can come across to your customers. You can spot sites from free hosting sites a mile away by the URL, and because of that you loss some credability, you don't tend to look professional. Personally I'd steer clear of it.
As with everything in this world, you get what you pay for.
Sorry to put a downer of free...afterall free is my favourite price =D
What Ive done with my design business is we were on host with a very expensive host, one day they needed re-design, we did it for them for free but wanted free hosting. They accepted... Maybe you can do so?