That is pretty weird. First of all, I am not quite clear about the status word. It looks that 8080 should send 0x23 status word during the interrupt acknowledge cycle (see page 2-6 here).
Next, I am 99.9% sure that clones work correctly with 8259 PIC, which does exactly what you've described: It keeps the INT line active until it receives 3 interrupt acknowledge pulses, allowing it to feed CALL instruction to the CPU. This effectively results in INT line being active for 3 consecutive bus cycles.
So perhaps there is an issue in the way you do the status word decoding?