Per ANSI 5010 837P, Appenix C, Page 8, GS06/GS02 is determined by the sender, subject to the constraint that they must be unique within a given Interchange (ISA12/IEA02 pair).
The documentation for GS06 recommends an unspecified period for which GS06/GE02 will be unique.
There is no wording in the definition GS06/GE02 concerning the receiver, and since the wording specifies that this number and any period of uniqueness are at the sender's discretion, I take this to mean that any rejection by any receiver for any reasons other than format (unsigned positive number with 1-9 digits) or not being unique within a given ISA12/IEA02 pair is not compliant with the standard.
Specifically, a compliant receiver may not specify (or enforce) any period of uniqueness to the sender. May a compliant receiver of an ANSI X12 Functional Group reject that group solely because GS06 was not unique within a time period not specified (or agreed to) by the sender?
Per your question:
May a compliant receiver of an ANSI X12 Functional Group reject that group solely because GS06 was not unique within a time period not specified (or agreed to) by the sender?
No, if no trading partner agreement has been established regarding the time period for unique functional groups, the receiver may not reject solely on the non uniqueness value of GS06.
With regards to uniqueness, the standard is clear.
X12.6 APPLICATION CONTROL STRUCTURE
3.9.1 Functional Group Header and Trailer
In order to provide sufficient discrimination for the acknowledgment process to operate reliably and to ensure that audit trails are unambiguous, the combination of Functional ID Code (GS01), Application Sender's ID (GS02), Application Receiver's ID (GS03), and Functional Group Control Numbers (GS06, GE02) shall by themselves be unique within a reasonably extended time frame whose boundaries shall be defined by trading partner agreement. Because at some point it may be necessary to reuse a sequence of control numbers, the Functional Group Date and Time may serve as an additional discriminant only to differentiate functional group identity over the longest possible time frame.
Per the standard, this is set with a trading partner agreement. The sender is responsible to implement uniqueness according with the trading partner agreement. If the receiver requires additional discrimination, the standard recommends the additional usage of the functional group date and time.