To start, this is not a request to get more gear, but a request to get less gear more quickly.
Consider this scenario: you just need 2 more stun guns to bring a character up to G12, but you have reasons not to want to farm them with energy, so you decide to request them from your guildmates. I will often see 2 get donated within the hour, but then you have to wait until 3 more get donated or 24 hours have passed.
One suggestion is to change it so instead of requesting exactly 5 stun guns, you instead get a slider so you can request 5 or fewer (other gear pieces would keep their current max amount). This way you can request the 2 you need and as soon as they are donated, you get them in the mail.
The other suggestion would be to add a "Collect" button on your request so you can collect what has been donated before the 24 hour period is up. This button will mail you what has been donated so far and then close out your request as if it was fulfilled.
With either option you would still be limited to 1 request per 24 hours, and you can still request the full amount of gear and wait the 24 hours to maximize donations if you want, but it adds some flexibility.