I can connect to my friends sometimes?

I can sometimes connect to my one friend on XBOX LIVE and other times I can't. My NAT is set to strict but that shouldn't matter seeing as how we are able to join parties and games sometimes but it chooses when we can. It's a damn hel when this happens. The person who runs the internet in my house is very tech savvy and refuses to change the NAT to open...and once he says no it's no..specially when it comes to internet. On the router we also have UPNP enabled...but still nothing. SOMEONE PLEASE HELP ME!