No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
If you do not carry a balance, I am not sure as to why you care about the annual percentage rate. I have never asked for a rate reduction so am not sure the procedure for it. I would just leave it alone though; not worth it if you do not need it.
Did they give any reason (account too new, too little spend, etc) for either decision?
Assuming that the decision cannot be changed, you have to decide the pros and cons of closing. It sounds like you might need it as the only non-store card you use. If that's the case, then I guess you just have to accept the denial, and wait until inqs etc go down and you can maybe get a better card