Homemade Arduino USB Host Shield
The most likely problem is that there's too much inductance in the D+/D- wires.

USB is picky. Running a USB signal through a breadboard, a pair of loose hookup wires, and a breadboard again is likely to degrade the signal to the point that it won't work.

You may be able to rescue this part by soldering the resistors directly between the USB breakout and the MAX3421E breakout -- bypassing the breadboard entirely. It'll be ugly, but it might work.

However, chances are that you'll probably have to respin the MAX3421E board with a USB connector on the board. If you do this, include a footprint for the crystal and associated capacitors on the board as well; the stray capacitance on a breadboard will often interfere with oscillators.