It really depends on what the problem is, who your target audience is for that site, and how easy it would be to put a hack in for IE7. IE7 has a fraction of a percent in market share for browsers these days.
You could also detect older versions of IE if you wanted to, and put a nice little message like "Yo, you're using an ancient browsers, you should upgrade".. (but in a more professional tone) yeah, my first three points should be your focus though.
I would say ignore, obviously sometimes your application is specifically for work and you know some of those users are on IE7 + windows xp, but the amount of crap you need to make it work with IE7!
Lots of themes that are sold professionally on sites like themeforest etc do not support IE7 and now IE8. This is moving with the times. All the goodness that you get with modern web browsers, responsive UX etc are horribly broken with IE7.
If it were me I would ignore all versions of internet explorer because they've really just made a right old mess of corrupting the standard in some way. But that is just a rant, and I'm sure IE10+ is now useable. Still, wouldn't ever use it except for testing.
I'm having a problem with a page that I feel can be fixed, but those I've asked have not came up with a solution ?
IE7 continues to be used by some users unable to upgrade. The reasons for this inability is not down to us to judge, so a 'hey dude, get with the 21st century' could be rather rude, regardless of the levity or professionalism of the tone.
You really don't want to hear my personal opinion of old versions of IE, but they would mirror those of most webdevs I would imagine. I'm not allowed to swear, so I'll can it.
A message stating that the site supports IE8+, Chrome ..., FF ... etc would be a more positive approach. You could include a link to recent versions of browsers if you wanted too, but that's starting to make a meal out of things.
If you are able to fix issues for IE7 relatively easily with a polyfill / shim or two, then it's up to you - but keep an eye on the load times. These things tend to build up and bite you in the backside without you realising, a few hundredths of a second here, a few there...