If they won't lower your rate, shop for a different card and transfer your current balance over to the new card with the low rate. You'll have to pay a one time fee to transfer but it's better than paying 20% on your debt for months. Screw them for blaming the economy for not lowering your rate. You're getting bilked.
I have five different cards with varying aprs. They all have a 0 balance except our main card that we charge everything on. When I used to carry a balance, right after I bought a used car, (it was about 6k and I charged the whole thing intending to pay it off in about six months), I used a 0% promotional APR check I got from one of my credit cards to pay for it.
So now I had 6k sitting on a card at 0% for six months and of course, things came up, unexpected expenses so my projected pay off got pushed back a couple of months. After the six months were over and my promotional period ended I had about 2500 left on the card. The APR jacked itself up to about 29% and I freaked.
So I transfered the balance to a card with a 9% apr that I hadn't used in a few years by going to the bank website and checking out their offers for balance transfers.
What's funny was as soon as I moved my profitable debt away from that once card company to another, they lowered my apr a bit and sent me transfer checks to try and get me to bring the debt back "home".
Long story short. Don't be married to one credit card. Play them against each other to get yourself the best deals. Find another card with a better rate and move your debt there. But I will caution you to READ THE FINE PRINT!! Some companies charge crazy amounts for transfer fees. Find out what those charges are before you take the deal. Some want 2% of the total debt in fees with up to a max of $50 and some cards will charge you 5% of the total debt with NO MAX which means, depending on how much debt you have, the fees could be more detrimental than keeping the old high apr until the debt is paid off.
The only way I've been able to get a credit card company to lower my rate was to threaten to close the account, or by transferring my balance away and having them come chase me down with attractive rates to get my debt back.
Since you don't use the card anymore already, they can see that and they know the only way they are going to make cash off you is by keeping your APR high. When you regularly use a card they get money each and every time you swipe and are more likely to lower your APR since you're already providing them income.