Thanks for telling me more!
So dada2 denoise-paired should produce stable ASVs, however, depending on what settings are used to run it, these results are not guaranteed to be identical. Take a look at this discussion multiple dada2 runs:
The main issues are --p-pooling-method and --p-chimera-method both of which can lead one sample to affect another, results in the change you describe when omitting samples before this process. See the docs
It's worth noting that the exact counts will change, the major biological results should be the same for dada2. If adding/removing a sample changes the ASVs a lot, then that's a problem and something else is going on!