Limited time from Awake to UART transmission

I am using S2C in sleep mode SM = 1 (Pin Hibernate), API1. An MCU is attached to the outside, the SLEEP_RQ pin (TH pin 9) is set to Low every 30 seconds, and a packet of frame type 90 is sent from the UART.
At this time, coordinator will not receive packet unless it takes about 1 second from setting the SLEEP_RQ pin to LOW to transmitting by UART.
I would like to shorten the awake time from the viewpoint of power saving. Is there any limit to the time from Awake to UART transmission?
Please let me know, thank you in advance.

The parent router needs to have the same sleep and wake times as the end device. You also need to look at the poll rate and adjust it.

Thanks for the information.

But the coordinator is always on without Sleeping. Do I still need that setting?

Xbee2 low for transmitter by UART from setting SLEEP_RQ to shorten the awake Time from the viewpoint

Yes you do. That is how the network know how long an End device is sleeping and keeps it in its child table. It also know from these values when an end device is going to check in and how long it should hold the data in the buffers for.