Declare victory and move on
The law of diminishing returns is the point at which the amount of benefits gained is less than the amount of money or energy invested. My experience with my clients is that sometimes it's easy to lose sight of this rule. Like a dog with a bone, sometimes we'll encounter a problem that we're unable to solve completely, even if the solution is a big improvement.
I was recently working with a client on implementation of their new AMS with a new financial management system. The client's ideal state would be a direct integration between the two systems. The proposed solution would be somewhat less than complete integration, so at first glance, it looks like we're not getting what we want and therefore should be pushing harder to achieve the desired state. But upon further investigation, the proposed solution would be a huge leap forward compared to the current state. So while it's not a complete win, it's a really dramatic improvement.
My advice to them? Declare victory and move on! What little additional benefit gained by "absolute perfection" was not going to justify the time and expense to get there.
Sometimes, a solution requires that we pour everything into it, to get it just right. But more often than not, "good enough" really is good enough. Don't get caught breaking the law (of diminishing returns).