Ensure that you pick your clones as soon as you see them and do a single colony culture. when your cells are 80-90% confluent, it develops resistance to the antibiotic and the clones expressing your gene is lost. So pick them up when they are 50-60% confluent and immediately sub-culture them separately.

I've had a similar experience of establishing cell lines and still found Flp-in cell lines to be much better and more efficient than the alternative. As above I'd first recommend taking steps to make 100% sure that you're not getting mixed colonies. After transfection I'd typically plate out onto 10cm plates at a variety of concentrations, so that when colonies developed there would be a density available to me where they could grow to a healthy size with minimal risk of cross-contamination during selection.

Also, consider increasing your hygromycin dose... I had a similar problem of HeLa cells losing their gene casettes over several passages, and my cells tolerated a concentration of 0.5mg/ml absolutely fine and this seemed to help in the maintenance of the expression, although I understand if your cells may not be as hardy as HeLas. 

Finally, as a last resort, consider re-enriching your cells which begin losing expression, just plate them at a low density and select for single colonies again and screen those colonies for stable, inducible expression. On the plus side you'll further enrich for the cells which are best and most stably expressing your vector, on the down-side it's another step of clonal enrichment which carries the risk of enriching for unwanted mutations or other differences from your control cell lines. Obviously you can (and should) compare your cells to un-induced controls of the same line but it's a judgement call, really.

Hello. Does anyone know where I can find a reliable protocol for using the Flp-In system? Geo