Absolutely Not! There is no such thing as a 48 hour rule.
There are no time limits for obtaining the signature on the DA FORM 4856 Counseling Statement. However successful counseling occurs as close as possible to the event (see extract below).
The fact that a counseling statement is dated for the 16th but not administered until the 22nd does not void the counseling or the offense.
However if a Counselor was to wait an excess period of time to counsel a Soldier (say 30 days), then it could be seen as less than professional and senior leaders might question the motives of the Counselor.
Extract of ATP 6-22.1
Specific Instances of Superior or Substandard Performance1-6. Often counseling is tied to specific instances of superior or substandard duty performance. The leader uses the counseling session to convey to the subordinate whether or not the performance met the standard and what the subordinate did right or wrong. Successful counseling for specific performance occurs as close to the event as possible. Leaders should counsel subordinates for exceptional as well as substandard duty performance.