I agree with @Haalcyon, changing your password on a regular basis is good. You might also really want to know what type of security your wireless router is set to... personally I use WPA/WPA2/FT PSK. My router also does dual channel, so it has both 2.4ghz and 5ghz bands... I can assign different names and password to the different bands. I just removed my Wi-Fi network and reconnected to test... there is no remember password setting, but mine always reconnects everytime I come home or turn it off or on again.
Not knowing that specific router, I'm wondering if there is a setting in the router that requires them to enter the password when they connect everytime. Did they give you a different Admin password, or is that the same as the password they gave you to connect to your network? You should have different passwords to log into your router as an Admin... the Admin is required to log into your router to change other internal settings like the security and passwords to connect to your secure router.