reCaptcha works only randomly on Contact Form 7

reCaptcha included with Contact Form 7 seems to create a race condition conflict with WP reCaptcha Integration that we use to protect our login form. Half the time, the contact page loads with the reCaptcha and half the time it loads without it and the issue is that people cannot send enquiries using our contact form whenever Contact Form 7 cannot render reCaptcha. This is highly problematic since we lose valuable contact information.

Anybody has any suggestion to try? I tried nearly everything I could Google up over the last 2 hours, it still only works randomly.