Your sentence is an excerpt of the following article, right?
اينترنت ملي يا اينترنت ايراني ؟
http://www.iritn.com/ITshow-news-10744.htm

If that is the case, پیوسته کاران in the aforementioned context means those who constantly work with or, better to say, use Internet services.

Examples:

Also, these contracts are made to cater to the needs of constant Internet users so the rates are more than what an occasional Internet user would expect. ...

urther, with big breakaway, follows the private company StarNet, providing services to 13.9 % of constant Internet users. ...

Aside from that, there is Google checkout which has been proven effective among constant internet users.

I ggogled the suggested equivalent, the result was the cited examples plus 39897 similar ones.