Russell Olwell, of Eastern Michigan University, offers some sage advice in Inside HigherEd.
The ability to take rejection and use it to improve your grant writing practice is the difference between many faculty members who write one proposal and give up, and those who persist to become funded principal investigators (PIs)…
The first key to dealing with rejection and negative feedback is to plan for it in advance and build it into your schedule. If you are interested in being funded by a program, you need to commit to applying for it at least twice (if not three times). This does not mean that the first attempt is half-hearted, but that the plan is to apply, get feedback, and use that feedback to strengthen the proposal.
The article is definitely worth reading.