The tiny screws that hold the denture to the implants keep coming out. Two in the past two weeks.

Hi:There might be incorrect bite pressure on the top denture.  I suggest to have your dentist check your bite and use a torque driver to tighten the screws.Best,Dr. Maddahi

Hello,
If this is a temporary denture it is normal to have some issues, but not as often as it might sound from your question. If that's the case, your Dentist should provide you with factual reasons of why this is happening, e.g. are the screws properly screwed; is the implant space distribution adequate for your denture design; are the Implants ok; or more importantly, is the bite right and stable? Some of these are the most common reasons why the patients get their temporary dentures loose. Hope this helps. 
Dr. Franco
DentArtist Clinic