Is there a time limit that someone must complete an FAA practical exam by if issued a notice of disapproval?

The previous responses, while correct, do not entirely answer your question. It is correct that the applicant can retest almost immediately after failing the practical test (see § 61.49 above.) The applicant can also retest 6 months later, as long as he receives additional training, another endorsement and his knowledge test is still valid. HOWEVER, there IS a 60 day time limit to complete the retest if the applicant wishes to recieve credit for any areas of operation passed on the first practical test. Example: a private pilot applicant completes approximately half of his practical test - successfully starting out on a mock cross-country, diverting, etc. However, while performing a power-on stall, he freezes on the controls, resulting in a steep break and incipient spin. The examiner is forced to intervene to regain control and pronounces that the practical test is now failed. At this point, the applicant can choose to continue or terminate the test. After landing, the examiner/inspector will issue a notice of disapproval listing the PTS Areas of Operation that were unsatisfactory. Additionally, any Areas Of Operation that were successful will also be listed. Assuming the applicant recieves additional training from his instructor and another endorsement for the practical test, the applicant can take his Notice of Disapproval to the second checkride and recieve credit for the Areas of Operation that were successful on the first test. Consequently, only the failed Areas of Operation and/or any untested Areas need be tested on the second test. However, the applicant may only recieve credit for the successful Areas if this retest is taken within 60 days of the failed test. Past this 60 day period, the applicant is entitled to retest, but he/she must retake the ENTIRE practical test, including oral and flight portions. Final note: the examiner or inspector IS entitled to evaluate ANY areas of operation at any time, even if it has been less than 60 days and the applicant successfully passed these areas of operation on the first test. Hope this answered your question, and good luck!

Check the FARS, but I believe you can retake the exam after a CFI has signed you off as ready to go after remedial training and your medical is still valid.