As the title states, subplots with equal aspect ratio drift around within the figure when the canvas is redrawn with figure.autolayout set. The following code demonstrates the issue

import matplotlib.pyplot as plt
plt.rcParams['figure.autolayout'] = True

fig = plt.figure()
ax1 = fig.add_subplot(121, aspect='equal')
ax2 = fig.add_subplot(122, aspect='equal')
fig.canvas.mpl_connect('button_press_event', lambda event: event.canvas.draw())
fig.canvas.set_window_title('Click to redraw canvas')
plt.show()

The issue doesn't appear to occur with the default figure size, but if you resize the window horizontally the subplots drift around with each redraw until eventually settling on a position.

Platform: Windows 7
matplotlib: 1.5.3
python: 2.7.12