120v to 24v 40va transformer damaged, replaced with 120v to 24v 15va transformer
Unless you actually measure the current required by the system when fed with a suffiently-large transformer, you won't know if the smaller transformer will work reliably.

Based on your description, I would suggest that the replacement transformer at 15VA is far too small and you really do need to obtain a 40VA transformer.

If you are having problems finding a suitable transformer, why not visit your friendly neighbourhood HVAC company.  24 Vac transformers are standard in HVAC systems and every furnace / air conditioning shop that I have ever dealt with stocks 24 Vac transformers in various sizes.