Yes, if that Soldier is within the qualification standards of AR 350-1, the commander can deny a Soldier the ability to take a Record APFT,
A Soldier may desire to take a “FOR RECORD” APFT because they want to improve their promotion points. Some commanders feel that you should have tried your best on your previous record test and should not be given the opportunity to take another record test until you are required to test again per Army Requirements. Keep in mind this is a Commanders program. The Commander can administer the APFT “FOR RECORD” test as often as they like. See AR 350-1 paragraph 1-24.
If there are extenuating circumstances that prevented you from doing your best on your last “FOR RECORD” APFT, then you should consider putting togehter a memorandum for the commander explaining the reason behind your request or you could ask to see the commander on open door policy and explain your case in person.