Why a slate slips
On an older slate roof the fixing may simply have reached the end of its life. Nails corrode. Battens can soften. Occasionally the slate itself breaks around the nail hole and drops.
Wind can finish the job, but it is often only exposing a weakness that was already there.
Look at the neighbouring slates too
If one slate has gone, I would not automatically assume the whole roof is failing. I would, though, check the surrounding area. A line of loose slates, repeated previous repairs or several broken nail holes tells a different story from one isolated casualty.
Repairs should suit the roof
There are proper ways to secure a replacement slate without smearing the roof in sealant. The exact method depends on access and the existing slatework. On a visible front elevation it is also worth matching the size and colour reasonably well; odd modern replacements can stand out badly on older properties.
After high winds
If a slate has fallen after a storm, have a quick look from the ground for anything else sitting proud or out of line. Do not climb onto a wet slate roof. It is easy to turn a modest repair into broken slates and a trip to hospital.