Can I get HELOC or Refinance on a Condo that wasn't approved for conventional loan

[Chioma Okonkwo]

Hello Sirs and Madams,

I'm new to property ownership. I am trying to purchase a Condo in Houston on Conventional loan but midway the lender pulled out because the HOAs master insurance policy does not meet their lending requirements. I got an option for a NQ Mortgage with 15% down, which I am willing to go with but my concern is since there is a conventional lending limitation on the property.. would I be able to refinance this property assuming interest rates go down to 4% next year? The NQM lender itself allows refinancing but my concern is the same HOA insurance issue will probably make the property ineligible for refinancing. In which case am I tied to this lender at a high 7% rate for the term (30 yrs) of the loan? Also, I'm not sure how Heloc's work.. but is it possible to get a HELOC or home equity loan on a property that cannot qualify for conventional lending? I just don't want to tie money up and unable to pull out any equity in 2/3 years.

Otherwise, I like the Condo. I plan to live in it for around 5 years and then rent it out thereafter. So I am not so much worried about selling.