You are provided a "run out" period at the end of your plan year (or date of employment termination, whichever occurs first) to submit reimbursement claims for any unclaimed eligible FSA expenses incurred within the plan year.
Depending on how your employer's plan is set up, it is now possible to have up to $550 of unused funds roll over into the next plan year. Effective October 2013, the "use it or lose it" rule (which specified that any unused health flexible spending account (FSA) funds were forfeited at the end of the plan year) was modified to allow for a 2.5 month extension (grace period) to spend down funds OR a rollover of FSA funds. Under this modification, an employer may opt to allow for a rollover of up to $550 for FSAs, in lieu of a grace period.
Please check with your employer to verify the specific rules for your plan, and to see whether you have the option to rollover your FSA dollars.