First off, UART mode 3 is a configuration of the peripheral hardware, NOT the means by which you connect multiple processors. What I mean is this: IIC (SMBus), SPI, UART RS485 - these are means to connect things.
Mode 3, 9600 baud, 100KHz are the modes of operation of the things you use to connect things.

But with that nit-pickiness aside, you've answered the question. You are using the UART in multiprocessor mode. I'm presuming at this point since you didn't mention RS485 that you are connecting the CPU's together per the Cygnal documentation, which (in my opinion) misleadingly indicates that you can directly connect the Tx pins on ALL slaves together. I don't think so. You really need some sort of tri-stateable interface device, such as an RS485 transceiver.

That being the presumption, I'm not surprised that two slaves work but three do not. The Tx lines are fighting each other. These are NOT open collector devices and therefore cannot be directly connected together, even though the documentation suggests they can.

I think that may be your problem. Some other things to consider to troubleshoot situations like this - in general:
1. If it works with 2 but not with 3, what changes? Have you looked at any signals using a scope? Don't have a scope? If you're a hobbyist you're probably on a strict budget and can't afford one (even though good prices on used equipment can be had via ebay and the like). If you're an employee then convince your boss you need some tools. Had you looked at the Tx line you would have likely noticed some degradation in the signal levels.

2. What about software? Just because it works with 2 doesn't mean it works with 3, or 10. Timing problems can make something appear to work under limited conditions. All you said was that the system stopped working. Not much for us to go on. Did the master continue to transmit but not receive any reply? Was the reply garbled? Did the CPU's lock up? Did multiple slaves attempt to respond at the same time, causing data collisions? You see what I mean? There are many more questions you can ask. The symptoms help define where you need to look next.
Hope that's helped.

When I searched this section of the forum I found two matches for the string "multi processor". The first one mentions about taking the pin TX in Tristate mode. So someone has suggested configuring the TX pin in open-drain config and using an external pullup. I tried that also but still the same problem. Now will try the second option suggested there that is to change the port configuration dynamically.
Please let me know if you find anything erroneous in my above statements ! or let me know if you come up with any other suggestions.
Thanks again.
regards
Ashish

Has anyone tried connecting 9 or more 8051 s
in multiprocessor mode?