Coordinator SP setting breaks bi-directional coms

My question relates to the SP (Sleep Period) parameter on the coordinator end of a pair of associated XBees where the remote is using cyclic sleep mode. What appears to be the case is that as long as SP is non-zero on the coordinator, it won’t send “direct” messages, only indirect (the result of a poll request). Immediately after the remote wakes up, a bi-directional ”conversation” is possible. But, if there is much idle time, the coordinator stops sending and will only send again if the remote goes back to sleep, wakes up and polls again (or something like that). This was confirmed by Digi tech support. Coordinator’s SP has to be zero for bi-directional coms. This is not useful behavior. In order for the cyclic sleep to be of any use, SP must be non-zero on both ends. But in order to make full-duplex communication possible, SP must be zero on the coordinator. Clearly it cannot be both zero and non-zero, hence my conundrum. And it is not practical to change the coordinator’s (USB XBee on a PC) settings on the fly as there is no code running anywhere to do it. The host PC is serving only as a dumb terminal. Any ideas?