I would suggest to clean the sim card area where the pins make contact with the sim card itself. However, you said you already did.
Other then that, check to see that the golden prongs are all lifted and at the same level. Maybe one of them is bent in too much and is causing bad contact with the sim.
Last thing to try is to reset the network settings.
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[http://vkrepair.com/iphone-7-sim-card/|Here is a good guide for sims]
I would suggest to clean the sim card area where the pins make contact with the sim card itself. However, you said you already did.
Other then that, check to see that the golden prongs are all lifted and at the same level. Maybe one of them is bent in too much and is causing bad contact with the sim.
Last thing to try is to reset the network settings.