To be accurate, the loss was automatic on divorce, based on a newly realeased Letters Patent addressing the issue of divorced royals.
On Aug 21, 1996, the Queen issued Letters Patent which decreed that a style received by a spouse of a member of the Royal Family on their marriage ceases at the point of divorce. The Wales' divorce was finalized 7 days later on Aug 28, 1996.
Clearly the decree was done in direct response to the upcoming Wales' divorce, but was also to set the precedent for a new bigger issue - that is, what title should remain when a non-royal woman divorces a British royal prince? The only previous 3 senior royal divorces of the 20th century - The Princess Royal in 1992, Princess Margaret in 1978, and Victoria of Edinborough in 1901 - all were different cases because the wives in question were HRH by birth, not marriage. They simply kept their pre-marriage titles.
The Queen and her advisors obviously decided that - in an era of 50% divorce rates - it was better to nip this issue in the bud before there were numerous ex-wives with HRH titles running around. And I think that was a smart move, for lots of reasons.
First, a divorced woman is no longer part of the royal family (Diana was an exception as the mother of the future king), and can do whatever they wish. The Court doesn't have much control over their actions, behaviors or words anymore. But if they kept HRH, their actions would be directly reflected on the crown, which could cause lots of problems if the ex-wife in question was a loose cannon. Let's say Sarah York kept her HRH, but decided to become an advocate for - I don't know - abortion rights. Now you have a royal princess/duchess taking a stand on a highly charged political issue, and the Crown can't really do anything about it. Very bad indeed.
Second, what happens upon remarriage? Does the woman give up her HRH title then?
Third, I believe holding the status of HRH conveys lots of perks and priveledges - such as royal security, right of use to Queen's flight, right of use to diplomatic resources when travelling abroad, diplomatic immunity as a member of the royal family. None of these things should be accorded to a person who is not a working royal.