First, “copyright claims” and “copyright strikes” are not the same at all. A copyright claim does not affect the good standing status of your channel, it simply means your video contains copyrighted material.
Copyright claims are easily lifted with the license you buy from AudioJungle. Most third-parties have a dedicated form to do just that and the process typically takes a few hours (the video should be set to “unlisted” in the meantime).
Now, the fact that the author doesn’t know why you’re getting those claims is worrisome. It either means they’ve registered with ContentID and don’t understand what it implies. Or, it could be that the author had left their music unprotected and a usurper fraudulently registered their music in their stead. It’s also possible that it’s just a false positive detection, though I don’t know if that’s such a prevalent issue. You may want to check out the copyright claim that was issued and see if the author matches the AJ author.
Regarding multi-use, @AnimSet is right there is no multi-use license for music. There are workarounds though. If the intro is always strictly the same with no modifications whatsoever and slapped as is in front of your videos, then the intro would be considered as the end-product and could be used in any number of videos.
If your intro has even slight modifications (different titles or other texts, different images,…), then they would be different end-products and would each require their own license. There is however a “series policy” that allows you to use a single license for up to 52 episodes (within a year) of a same series.
Hope it helps