Hi BB,

Initially it is the responsability of the strapper to tighten the girth and check the saddle and all accessories.
The trainer is then meant to double check in the mounting yard once the horses have paraded prior to the jockey mounting, but there is no rule stating this as such.

Finally, most professional jockeys will triple check just prior to mounting.
Some have been known to gallop their horses to the barriers, jump off and check it - then jump back on, although this is rarer.

The saddle can slip for a couple of reasons.

1. Naturally some horses "puff up" knowing that the saddle is about to be tightened and give a false sense of what is tight enough to the strapper.
You should be able to snuggly fit three fingers between the girth strap and the horse - but no more.

If the horse has "puffed up" or taken a deep breath, then often the saddle will slip, which is why some jockeys will jump off at the barriers to double check after galloping the horse.

As far as I know there is no rule about this, but there could be somewhere in the rules of racing.

2. General equipment failure. But it is up to the jockey to make sure his saddle and girth straps etc are in good nick - most have professional caretakers which clean and check the equipment these days.

hope this helps.