I'm also in online therapy and we write (not technically text, but similar) constantly, meaning typically something every day. While that's rare in traditional therapy, it's increasingly common in online therapy where most of the communication is often written, like on services such as BetterHelp. Ours is a weird hybrid of Skype and chat, with the occasional email card thrown in. There isn't a limit per se, but typically I do not write on weekends.