Q1, the 2N3906, fully discharges C1 each time the trigger line goes low, restarting the timing cycle. The values of R1 and C1 determine how long IC3 maintains the transmitting mode after transmission ends.
This interval should be long enough such that the converter doesn't switch directions while sending characters containing long sequences of zeros. On the other hand, it shouldn't be so long that the converter misses received characters. The interval T in seconds is T=1/R1C1, where R1 is in ohms, and C1 is in farads. The flow control responds within a few microseconds after transmission commences, so the converter does not miss any bits at low and medium data rates.
The application for this circuit operates at 14,400 bps. Figure 2 shows the timing of the serial and flow-control lines. The entire circuit can fit into a DB-25 (or even a DB-9) back shell.