fungus:
There's a simple way to find out if current is the problem - measure it!Watch the voltage on the +5V pin, see if it drops under load.
I thought about it since first reply. So I have measured it and doesnt seems to be problem - voltage is constant at 4,94 V.
But idea inspired me that there might be peak voltage drops in very short times - e.g. in 1 microsecond or so - this will definitely affect hi-speed SPI that runs in 8 Mhz. I also looked at 5V voltage under oscilloscope, but seems linear.
I will try adding 1000 mikroF capacitor at input, maybe it will help.