Without knowing too many details, the fact that you own the property already shouldn't matter much on whether or not you qualify for a construction loan, home equity loan, home improvement loan, or whatever else anyone wants to call it. There are technical differences between them all, but they mostly accomplish the same thing. The only thing I can think of is maybe that bank's internal loan policy is rather strict and they do not like getting involved in these types of projects, which can carry some significant risk. Just depends on the bank.
A bigger question is how big is the renovation project? If it's a significant sum of money comparative to the as is value of the home, most banks will get the property appraised "as completed" and then set you up with a construction loan based on percentage of the as completed appraised value. That's usually around 80% but federal regulation allows banks up to 85% on those types of projects (assuming it's a 1-4 family residence). If the bank you're working with isn't wanting to do this project, there are other banks out there that will. It's pretty normal financing.
