In Proteus 8 simulation of the PIC16F84A assembly code (.asm), any setting (BSF) or clearing (BCF) of the pins  clears pin RA4!
It has been commented on that your questions could be asnwered better by the Labcenter company that sells Proteus.

You do however raise an issue encountered but many PIC users. That is the Read-Modify-Write (RMW) problem on output bits using the bit set and clear opcodes. Most older 8-bit PIC16F controllers have this issue. 

It has been addressed on the enhanced PIC16F and all of the PIC18F 8-bit controllers. These devices have a separate output latch registers for the GPIO ports.

The RMW problem arises because the GPIO port is used for reading the input state and setting the output state of all of the bits of the GPIO port even when using assembly opcodes that involve only one bit.

This problem is compounded when GPIO bits are configured for an analog functions and as a digital output because any pin configured for an analog function always reads from the PORT register as a zero regardless of the state of the digital output.

For the PIC16F84A PORTA, RA4 is an open-drain output, unless there is an external pull up resistor this bits will never read as a one. As you have found it is all but impossible to use the bit set and bit clear opcodes to change other bits on PORTA without affecting RA4.

The best workaround is to use a controller with output latch registers for the GPIO ports.