If all that changes is the name in the URI then it sounds like a DNS issue to me.
Not sure how your ADSL is set up; is your traffic balanced over the two lines so some requests are going over one and some over the other? If this is the case, does the external IP of your web server point to only one of your ADSL interfaces, if so which one?
If it were ADSL-A for example, does the problem only happen when making a request and it gets balanced out of a certain ADSL interface like ADSL-B for example? Or only when it goes out of ADSL-A?
Seeing as you have a web server at home, do both lines have static IPs? If so, are they from the same provider? If so, are they in the same subnet?
Somewhere in here I expect is the problem, either a simple routing or NAT issue possibly.