Strange it hasn't been mentioned, yet. We would have to know the speed of a subspace radio signal for which we got figures in "Balance of Terror" and "The Enterprise Incident". Kirk's real time conversation with his superior in "The Alternative Factor" provides some clues:
BARSTOW [on viewscreen]: Negative. I'm evacuating all Starfleet units and personnel within a hundred parsecs of your position. It's going to be tough on you and the Enterprise, but that's the job you've drawn. You're on your own.
Assuming Barstow was not evacuating himself, this would indicate a real-time conversation (including video) via subspace at a distance of at least 326 light years.
Balance of Terror
Just prior to arriving near Earth Outpost 4 Kirk orders "Open a channel to our nearest command base. Quarter hour reports on our position and status."
KIRK: Are you continuing to broadcast tactical reports?
UHURA [OC]: Affirmative, Captain.
KIRK: And at this distance?
UHURA [OC]: Approximately three hours before receiving a reply to our first message.
(apparently the one above)
At the end of the episode:
RAND: We finally received an answer from Command base, sir. They say they'll support whatever decision you have to make.
Assuming that Kirk asked Uhura one hour after the first report to command base, it seems that it would take a subspace signal 2 hours to get to Starfleet and 2 more to get the reply.
Janice's "finally" isn't clear. Either it suggests that it's really quite some distance (conversations with Kirk's superiors light years away usually occur in real time!) or
it took Starfleet a while to discuss what orders to relay to Kirk.
The Enterprise Incident
KIRK: You understand that Starfleet Command has been advised of the situation?
TAL [on viewscreen]: The subspace message will take three weeks to reach Starfleet
[and three more to get a reply]. The decision is yours, Captain. One hour.
Now that really takes some time. I'd find it hard to believe that subspace technology had gotten worse.
However, Tal's information could be wrong and Starfleet somehow made the Romulans believe that it would take that long. Kirk doesn't comment on the time a reply would take.