In addition to the diodes, put a resistor from the Rx pin to ground. As it is, due to the diodes, there is no conduction path to pull the pin low. Its capacitance will keep it high for a short period of time until enough charge leaks out (through the leaky Schottky diodes) to register as low. The resistor solves this. I'd start with a few kohm, like 3.3k and go from there. Viewing the Tx pin and Rx pin waveforms on a scope would be highly beneficial.
Edit: FrankBuss beat me to it, and I forgot that TTL level UART idles high, so you want a pull-up resistor (as Frank said) not pull-down,