The cords on the Peak Design connectors will wear. Peak Design advises you to periodically inspect them for wear and replace them when necessary. The new version 3 connectors have a red inner core and if it's exposed, you need to replace them. They come with a tag attached with instructions. I don't know about how you tell if the older thicker connectors need replacement.
The most reliable connectors are stainless steel split rings. But he ones on many straps are too thick for the Fuji lug holes, so you need to replace then with 16mm split rings. To keep the rings from scraping the body, you can use those leather shields that come with the camera if your strap connects like the factory straps or you can get rubber o-rings that have a hole just large enough to fit over the lug and are thin enough so they don't block the lug holes.
