Unless you’re highly motivated or oblivious to pain or muleheaded (and yes, it can be hard to distinguish among those traits at times), most of your running injuries are going to be in those early stages, where how to proceed is based on judgment calls and guesstimation.
How much or whether to cut back in those cases will depend on lots of factors. Do you have an important race coming up in a month? In that case, you might be more inclined to stop for a day or two to see if that will calm what’s become a persistent ache. That way, if the time off pretty much takes care of things, then you can get right back into race training. Of course, if you’re in a non-race phase, then there’s not as much urgency to preserving your fitness, so it could be easy to get yourself to take some downtime to let things heal.
Then again, you could make the argument (I certainly have!) that, with no important races in the near future, it’s OK if this little limbo injury continues on for longer than it otherwise might if I stopped running on it. Especially if I’m going through a stressful period in other parts of my life, I’m willing to take a chance that a little strain won’t get any worse by running on it so that I can get the stress relief that running brings. In that case I’m aware that I’m probably prolonging the time it will take to be free of the niggle, but it’s worth it to me.
This sort of on-the-one-hand-on-the-other-hand discussion with yourself is, unfortunately, part of being a runner with any sort of injury. It’s why being hurt is so mentally draining and is reason alone to do your best to avoid getting hurt in the first place.