I do sympathise. I too have had this problem, and for what they are, those badges are very, very expensive. Strangely enough I found that this problem only occurred at the front hole on the nearside (drive side) of the tank. I can offer no logical explanation why this should have been so. I know that that this will be of no consolation to you, but it seems to be a well known and common problem. This particular problem has been raised several times on the BirtBike web site. My own solution was to reinforce the material surrounding the hole with some carefully applied body filler in order to give it a bit more strength, and to help spread the load. I have had no reoccurrence of this annoying problem since I did this. I would guess that Araldite or something similar would do the same job. The main advantage of body filler is that unlike Araldite, body filler sets very quickly, and is easier to apply. If you look closely at the back of the badge the first thing that you will notice is that the surface behind the two screw holes is not flat. And this in my opinion is what causes or at least contributes to the problem that you describe. The clip is quite springy, which I suppose it needs to be to hold the badge firmly against the tank. The curved surface on the back of the screw holes combined with the springy nature of the clip generates tension. Obviously it does not help that the hole itself is countersunk, and this an obvious Achilles heel that compromises the strength of the plastic in this area. The plastic that is used has no real built in elasticity, it is quite thin, inflexible, and brittle. The design and materials used on these badges is far from ideal, and we should not have to resort to devising methods of over coming these basic inherent flaws. The most annoying thing is, that these badges as you well know, cost about £30 per pair or more plus p&p. So, as happened it my case if one badge fails you have no choice other than to buy another pair because you cannot buy just one badge. You can see how much of a problem this is click the link below.
http://www.britbike.com/forums/ubbthreads.php?ubb=showflat&Number=514740John