The problem is not the design or something else.
"ABSOLUTE MAXIMUM RATINGS (1)Continuous output current +/-35mAContinuous current through VCC or GND +/- 70mA(1) Stresses beyond those listed under absolute maximum ratings may cause permanent damage to the device. These are stress ratingsonly, and functional operation of the device at these or any other conditions beyond those indicated under recommended operating conditions is not implied. <b>Exposure to absolute-maximum-rated conditions for extended periods may affect device reliability.</b>"So 35mA rating is not recommended long term.And the power supply pin only supports 2 pins at that current.Further design questions:Do you have 0.1uF cap on the Vcc pin of each shift register?Are you sinking current (low outputs) to turn things on? I would use TPIC6C595 (100mA per output) or TPUC6B595 (150mA per output).
Well, 80mA is greater than 70mA. As an engineer I would suggest something else. And did, if your load can work with the shift register sinking current from it to activate it. LEDs and motors work great that way.I even offer a board with a '328P and 1 to 12 shift registers to control up to 96 outputs.http://www.crossroadsfencing.com/BobuinoRev17/#LED-Driver
there are 15 pcb cards in system. Every 5 of them connected to a 40 A 12 V switching power supply.
"I have a 0.1 uf cap between latch pin and the ground pin."Get rid of it. Digital control lines should never have caps on them. There is an Ardiuno page in the Playground showing a cap like that; we have complained about it for years.0.1uF and 1.0uF from VCC to Gnd is needed tho.
"Do you think problem might be the instant change of power supply ? since 7805 regulator feeds from same power supply ?"Could be. Depends on how much of a current hit each motor is taking off the 12V line.Can you try adding a separate 5V to your system to power the shift registers?Examplehttp://www.mpja.com/5-Volt-DC-Plug-Power-Supply-4A-Regulated/productinfo/18520+PS/Keep the Gnds connected.I still strongly suggest a 0.1uF cap at Each shift register.
Use an oscilloscope.