"The more proposals we send out, the better our chances will be of getting funding!"
This is only sort of true.
Successful fundraising can be a numbers game. Take foundation proposals: For every 10 you submit, three will be funded per industry standard.
This ratio assumes, however, that you are applying to foundations whose interests align well with your nonprofit's activities. For example, if your nonprofit provides literacy services to adults and you apply to a foundation interested in children's reading and writing skills, you should expect a "no" from the outset.
Alas, submitting to a foundation that doesn't fit your mission only wastes your valuable time (because why work on a proposal that you already know will be declined?) and the foundation's valuable resources (because its staff or board still need to review your submission, no matter how far afield it may be).
Consider the following formula:
Foundation's stated interests + foundation's awarded grants
= your nonprofit's activities
In other words, what a foundation says it funds AND what it actually funds should align as closely as possible with the work of your institution. Thus, it's a great idea to seek out foundations that share your nonprofit's passion and mission. (See this post for more tips on finding the right prospects.)
In the end, go for quality over quantity. Because of the 10-to-3 rate of return, you certainly want to find as many suitable prospects as possible. Ultimately, however, if you only identify seven or eight possible funders for your program, then submit the very best proposals you can to these foundations. Tailor each proposal to meet the funder's guidelines.
Finally, remember to connect with the foundation before you submit a proposal --if the funder allows it. You'll be able to bounce your proposal idea off of the foundation staff and receive feedback as to optimal submission timing, proper ask amount, and whether your proposal idea will be of interest to the organization at this time.