Is there a specific reason to stick with the original "solution"? i.e. Backwards compatibility, other part(s) are reliant on that configuration, etc.? If not, I would say that's part of the normal design process.
Personally, just on a simple project I'll find myself refactoring either design or implementation until I've found a solution that works, but also is more efficient (the former being the most important) [red, green, refactor].
Take a more basic approach; Should you solve a problem in ASP.NET and keep brute-forcing problems, or move to [e.g.] perl where a library available would make it very simple to design? If the project doesn't have any other complications it probably makes sense to move to something that would make your life easier (as long as it meets the needs of the original project). However if, for example, the rest of the site is in ASP, it would stand to reason you would keep working on a solution instead of shifting the whole site over because of one problem (even at the expense of additional days of problem solving).