As someone who singlehandedly accumulated £1500 worth of prizes for a school raffle/prize bingo, I can assure you that many local business can and do donate.
I often found going in forearmed with the name of who I should speak to, a letter stating my request (& what the raised funds would specifically be used for) on headed paper (I note that you mention you have been doing this - it's not just to 'prove' who you are, it also gives the donor something to show what they have donated to; and allows them the opportunity to claim back some of the 'cost'. Businesses who have a set annual fundraising budget don't do it out of the goodness of their heart - a certain amount is tax deductible!).
Practice your pitch, go in smiling, explain who you are and where you are from.
Say you are looking for donations for a charity event and that this doesn't necessarily have to be goods or cash, it could be services, promissory notes, even promotional goods.
Also, think outside the box! Ask EVERYONE (within reason! Clearly you don't want free tix for the local strip club as a school prize)
Some donations I accumulated in recent years:
Family tickets for cinema/local attractions/theatre
Activity ticket/vouchers (golf, gokarting etc)
A big bag of butcher meat!!
Gift vouchers for beauty/hair treatments
Books/toys/CDs from independents
Restaurant/takeaway vouchers
Driving lessons
Fashion accessories/jewellery
Food hampers
Booze (one particularly weird one was from a tyre specialist, who gave me 2 bottles of really posh whisky that he had under the counter
I think he said they had been a gift from a sales rep who had been in during the week!)
Household goods
Handknitted/crafted items
Supermarkets usually have an annual budget and someone who deals with it. In our local ones it tends to be the person who is often at the front of the store handing balloons to kids etc. Sometimes we've been lucky and they've given us huge boxed toys (old stock maybe) other times its been a bag full of packets of sweets.
I've even managed to aquire free books of raffle tickets along with a donated prize!
You don't have to ask for prizes : you could ask for other donations. Things like tea coffee biscuits usually come out of YOUR budget, if you can get these for free, its one less thing that the PTA has to fork out for
You can phone round places like local cinemas etc, sometimes you get lucky, sometimes you don't.
If someone says no, don't take it personally, stay friendly and polite - always ask "would you mind if I popped by to see you next time?"
They may not be in a position to help now but a polite response to the no now means that in the future they might say yes. I have even been in the position where someone has said they can't, I have said no problem, finished the chat in a friendly manner, invited them to pop in to the event and by the time I left; went out the door with more than I went in to ask for!
Don't worry about the NOs, I know it can be disheartening sometimes but its not YOU they are saying no to. They probably either genuinely can't afford to donate now, have a policy to only donate to certain charities, or have already been so generous with other donations that a budget they had set has been used up
You could always ask if they could put up a poster advertising your event?(including a plea for donations of course!)
Oh, and as for being flummoxed by a reason behind a NO response; there will always be people who say no. Some will do it simply, some will give a reason; either is entirely their prerogative. Your best response is honestly to just remain friendly, depending on what their reason is you can say you understand/joke that you'll just need to get in earlier next time etc. If you have been polite and explained exactly what & who your are fundraising for, whilst they may or may not wish to support such a thing, they will be far more likely to respond positively either now or in the future if you are courteous.
I have completely waffled on and no doubt others have said all the above in the time it has taken me to type this on my phone, if so : I apologise !!
Have fun, and please share any weird & wonderful prizes you acquire!!