I've also seen new converts fall away rather quickly and suspected they never developed a testimony themselves - that faith brought them into church, nothing else. Still, I think that it's nearly impossible from the outside to discriminate faith and testimony clearly, and therefore I hesitate to generalize. Would generalisation not necessarily mean that all the people mentioned in church history like Sidney Rigdon and others who fell away after some years never had a real testimony either? A testimony can shrink and disappear, if it is not nourished properly, and how to proof afterwards that it even existed? You mentioned conversion and I think it's an essential aspect. I learned that for me, conversion is a lifelong process, and whenever I thought I'm already there and stopped moving (daily scripture study, personal prayer...), it weakened my testimony - and without continuing repentance I'd gone inactive in the end.