Does dental adhesive cream pose a danger to tooth implants for snap-ins?

You can absolutely use denture adhesive cream under your denture to assist with stability. You will not harm the dental implants nor the snap in component parts. 

From your description, it sounds like the inserts are getting distorted very rapidly after they are replaced.It could have something to do with the angulation of the implants or  The attachment system  that is being used.If you bring this to your dentists attention, they should be able to figure out a solution that will hold your denture firmly for more than just a week.I hope you found this information to be helpful,Dr. Champagne

There is no harm in using the adhesive. Use it for short period. There might be multiple reasons for denture coming out even though new attachments are fixed onto implants.
1. If denture is coming out only on biting. The bite with the opposite jaw needs to be checked and adjusted.
2. Depends on what type of teeth/ material is there on the jaw other than dentures- natural teeth or denture or Ceramic / Porcelain teeth.
3. Nylon cap Attachments are not picked up in the dentures properly that is why they are not fully engaging into implant attachments
4. Denture borders are not correctly extended either over or under extended. If extension is under- relining should sort your problem , if extension is over and denture is getting lifted specially while swallowing you need to get it trimmed more.

I suggest that you should visit a prosthodontist to fund out where the problem lies. Meanwhile there is no harm in using adhesive cream but don't put it in the areas where you have implants.
Hope that helps....