Ignoring credit scores and interest rates on loans for a second, how does this credit card benefit you? Does it have frequent flyer miles or cash back or rewards points? If it does, and it sounds like you have had it for awhile, try to assign $ values to the reward benefits that you receive and look back over the history of the card and see if that average yearly reward $ amount is close to $45 or not. If it is, then obviously you're not losing out too bad and can keep it since benefit >= cost. If the amount is well under $45 or you don't even have any type of benefit other than for the sake of your credit score, then I'd say ditch it (unless you are financing something in the NEAR future). Even if you are going to get a mortgage in the future, the ding will surely have recovered by then if you have other credit lines open and your credit is already excellent now.
Having the best credit score possible is neat but if you don't need to utilize the good score now (and you aren't getting benefits), then essentially you are paying for vanity. Keep in mind most of the lowest rates are already offered to 760+ or even 720+. e.g. if you are at 800 now and cancelling would put you at 795 next month, it likely wouldn't change anything.