AC won't start up because the exterior temp readout reads at 38 below most of

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the time and when it does start to move up in temp it won't go above 50 degrees but the AC will start working and works good. Than in a short time the temp starts going back down and than the AC begins to not working again. I have replaced the outdoor temp probe and the inside control box but the problem still continues. I don't know were to look anymore and would really appreciate some help.