There is no requirement to provide notification for an APFT test however TC 3-22-20 Appendix A states:
A-8. The commander should ensure that testing is consistent with regard to events, scoring, clothing, equipment and facilities. Testing should be planned to permit each Soldier to perform at his maximal level, and should ensure the following:
- Soldiers are not tested when fatigued or ill.
- Soldiers do not participate in tiring duties before taking an APFT.
- Weather and environmental conditions do not inhibit physical performance.
- Risk analysis is conducted.
This implies the command should provide adequate notice to ensure the best possible performance.
With regard to how often the test can be administered see AR 350-1 which states:
Commanders may administer the APFT as often as they wish; however, they must specify beforehand when the results are for record. The AA and Active Guard/Reserve (AGR) Soldiers will take the APFT at least twice each calendar year. A minimum of 4 months will separate record tests if only two record tests are given. The intent is for the Active Army and the AGR Soldiers to take a record APFT every 6 months. Mission requirements often prevent the even spacing of record tests. Therefore, commanders are encouraged to test Soldiers for record as close to the record test window as possible.
This means that if the commander will test more than two times in a year he can administer a record APFT within three months of the previous test (per your question). If there will only be two tests in a year then there must be at least four months separating each test.