Software implementation of a UART

[rmd]

I'm trying to build an appliance with two UARTS using a 16F877.
I have big problem with the UART implemented in software: when I transmit characters from a PC one by one or with a delay of 1ms between them, all goes fine. But when I try to transmit them without that delay, they are corrupted.
Using the library code from CCS (#use RS232...) corrupts characters too.
Here's my code (in CCS, for 16F877), for my getc routine:
If I use the pins 6 & 7 of the chip for tx and rx, it happens the same
I am pretty sure its a speed problem, but how can I fix it?

#define SERIAL_PORT 0x07
#define TX_PIN 0
#define RX_PIN 1
#bit txData = SERIAL_PORT.TX_PIN
#bit rxData = SERIAL_PORT.RX_PIN
// txData and rxData are mapped onto pins TX_PIN & RX_PIN of the chip...

char my_getc(void)
{
unsigned char c, bitno;
unsigned int16 dly = 104; // magic number: bit width at 9600bps
set_tris_c(1 << RX_PIN);
for(;;)
{
while(rxData); // wait for start bit
delay_us(dly/2); // to be sure its not a glitch
if(rxData)
continue; // was just noise
c = 0;
for(bitno = 0; bitno < 8; bitno++)
{
delay_us(dly);
c = (c >> 1) | (rxData << 7);
}
return c;
}

Whit this approach, I have also written a putc() routine, which works ok.
The magic number of 104us can be calculated at assembly time and not be hardcoded, but this is a test.

[PCM programmer]

What you're calling a "magic number" is really the bit period in micro-
seconds for 9600 baud.

You have somewhat less than two bit-times (208 us) between the
time when you finish receiving one byte, and the time when you
must detect the next start bit. I calculated this from:
Approximately 1/2 bit time is left after the last bit is sampled.
1 full bit time is left, during the stop bit.
Approximately 1/2 bit time is available if the next start bit is initially
sampled near the midpoint, instead of the beginning of the bit.
This adds up to approximately 2 bit times of "slack" time, between
the bytes.

You didn't show what you're doing between calls to my_getc().
You also didn't show your PIC type, or your oscillator speed.
You may have only 200 us (let's say) available between calls to
my_getc(). If you take more than 200 us to run other routines,
before you call my_getc() again, then you will miss characters.