I'm not familiar with WiMAX, so bear with me.
What are the hardware components of your network configuration?
Is there a WiMAX modem in your home/business which communicates signals to and from your ISP? Or is there a WiMAX adapter on your computer which communicates directly to some WiMAX station (beyond your direct control) miles away which relays it to/from ISP?
If there's a WiMAX modem in your home/business, does WiMAX modem connect to a home router to which your computers connect either "wired" or "wireless"?
I would look at configuration options of home router or in-home WiMAX modem for capability to setup logon credentials at those "choke" points for an always on connection. But once again, I'm not familiar with WiMAX. Love to know more about it.