We use the present perfect when we are announcing news (e.g., "There has been an earthquake in Mexico"). So the first sentence, which contains the news, is in the present perfect, and the second sentence reverts to the simple past because the speaker is asking about something in the past ("Where did she lose it?").

"Mum has lost her purse." = this is important now. We use Present Perfect to make a past event relate to the present. (Cool, huh?) "Where did she lose it?" = asking extra information. It's a past event, that's all. We already know it is relevant. If you say, "where has she lost it?", you are asking about not one, but several possible places where your mother has lost her purse in the past. In fact, it sounds like a habit. "Where has she lost it now?" means that your mother always loses her purse somewhere, you just want to know about this time.

In "Mum has lost her purse" "has lost" shows that she can't find it, but she may not know when or where she lost it. "Where did she lose it?" is asking about a single moment in time: the moment that it got lost. If you asked "Where has she lost it?" it would still be correct, but it would mean that she has lost her purse many times, in different places, and you want to know all the places that it has been lost. I hope that makes sense. Let me know if this needs more explanation. :)

Everyone's answer seems to be correct. My answer would be a tad (a little bit) different. The present perfect tense "has lost" indicates that she lost her purse at some indefinite time in the past, and the purse is still missing/lost (continues to be lost) up to the time of the statement. The purse was lost once, at a specific time and in a specific place (although the place is not known), hence the simple past tense. Regardless of whether my answer is right or wrong, I'm starting to get the feeling that I'm beginning to understand the present and past perfect tenses - imagine that... BTW - Has anyone seem my cell phone - it seems I have misplaced it ... again :)