It's completely down to the different companies when (if they have a set time), whether and how much they sponsor any team. Don't expect any reply at all either, as many won't even bother!
That said, I know many paint suppliers get their annual allocation for sponsorship decided on a calendar year basis. Something else to consider is that most sponsors have a good idea who they want to have using their products and will provisionally allocate stuff for them and their existing sponsored teams. If these preferred teams decide to go elsewhere, THEN other, lower ranked teams will be considered. As you can imagine, this adds up to not expecting to hear anything for quite a while! Be careful about pushing it too far in nagging them, as different people have different tolerance levels for this kind of thing & you may annoy them (& therefore lose a potential deal) if you call them every single week for 6 months.
If you're talking about non-industry sponsorship then your guess is as good as anyone elses!