First of all, we always keep submissions (unless your project exceeds the total allowed size for any project, which is unlikely) so don't worry. If you have selected a plan, which allows for 100 submissions / month and you receive 120 submissions in one month, then the 20 submissions will be available to you the next month (and count against the 100 submissions quota of that month) or you can upgrade to a higher plan to get access immediately.
If you have reached your total allowed file quota, you can either start deleting older submissions, or upgrade to a higher plan.
At Dropzone we treat our customers the way we like to be treated. The only two reasons for a company to offer an annual plan are to 1) be able to plan ahead a bit better, and 2) to force users to pay for a service they might not actually end up needing or using. The first reason doesn't convince us, and we don't want to force anybody to pay for something they don't need. You pay for what you use, and are free to cancel any time.