Another thing to consider is that in teaching, every single time you agree to something, you have to ask yourself "Am I ok with 30 of them doing this?" Or in the headteacher's case, hundreds of them.
When we're talking about just one child, it's easy to think 'well just give them one more sticker and explain they really have to look after it' but then you have to allow the same for everyone else.
Now we're in a situation where any child who loses their sticker is allowed a new one. How many times? Do they get to just keep coming back for more? In what timeframe? Is it just the day of getting it that they're allowed to replace it? What about the day after? What about if they've had it stuck on their bedroom door for a month then their sister rips it off in anger and they're really upset?
If they just get one replacement, is that one replacement per sticker, or one per month or year? Or one ever? Who is tracking who has had replacement stickers? Are the office staff creating spreadsheets? Or do they just have to remember who has had replacements? There's a lot to think about. If they mess up and accidentally give a second replacement out, you can bet some parents will demanding their child gets another one too. (Yes I GUARANTEE you these conversations would happen between parents). Do the parents have to email each time a replacement is required? That's a lot of emails to deal with. Not to mention the effort put into having to word the "sorry your child has had their allocated replacement allowance this year" emails, and dealing with being asked for exceptions and deciding if they're good enough.
I know a lot of people will read this and think "it's just a sticker, you're making it too complicated" or "you can just do it for this one child as a one off. You don't have to do it for everyone" but we're on a 9-page thread about stickers so evidently it IS a big deal and parents WILL complain. The one thing that riles people up the most is "unfairness" and children not getting the same treatment.
So now unless you want to give the teachers or office staff extra sticker-tracking jobs, you're signing yourself up for complaints and hassle by doing this. It's much easier just to say no replacements. You get your sticker on the day and that's it.
OP don't deny your child the chance to learn that feelings can hurt but they're ok and she will get through it. Learning to deal with disappointment and loss with a sticker is preparing her for how to deal with greater disappointment later as an adult.
I don't think that it's silly for her to be upset. It's important to her. But you can't protect her from negative feelings and then throw her to the wolves when she's an adult and expect her to deal with heartbreak and all the adult issues that come, when she's never had chance to learn with a sticker. Don't interfere with the perfectly natural way that children gradually learn resilience.
You don't need to dismiss her feelings but you don't need to fix it either. Be there for her and empathise with her. Then when she's 7 and she loses a toy she loves because she wasn't careful, do the same. And when she's 9 and her best friend falls out with her do the same again. When she's 19 and her boyfriend breaks up with her, she will come to you and know you are there. You can't fix it but you're there and she will know then that even though it hurts she will be ok.