Should I reapply?

If a law firm rejects me for a summer vacation scheme should I bother reapplying to it for a training contract?

I applied to all of the top 20 law firms for a summer vacation scheme and didn’t manage to secure a single placement despite being invited to attend several interviews. However, I’m still desperate to get a training contract with a leading firm so was wondering whether it’s worth reapplying to the firms that rejected me? I’m worried that if I don’t then my choice of firms will be really limited. Any sensible thoughts would be welcomed.