When connection lost, you can login its web interface? Is there any error in the log? Provide that log. Connecting to the modem directly works OK all the time? The router is new or it was working...

That's right. Good news for you. There is newer firmware released recently. Upgrade it and reconfigure it to see if the problem continues....

Any error message when you cannot login? Did you see the window asking for username and password? Try to clear browesing data first and login with the new password or try a different web browser or...

The printer is a new one? If it is connected to your PC directly, can you print? Printer's driver has been installed on that PC, right? Disable anti-virus and firewall first. Try again.

Try to update the driver of RT3070 in the link as below. http://www.mediatek.com/en/downloads/ The screenshot of your PC is in Spanish or some other language? I don't understand it... Don't forget to...

130506 is the firmware version? Verify hardware version. If it is V8, upgrade the firmware to see if it performs better. http://www.tp-link.com/en/support/download/?model=TL-WR841N&version=V8#tbl_j