> The H-1Bs however, in my experience, don't. Why might that be?

That is strange. In my experience, H1Bs are let go as quickly as natives if they are not competent. Of course, it could simply be a matter of the type of companies we have worked with. Again, see my (longer) response to the OP. I have mostly worked with Type 1 people I described there and have been fortunate enough to mostly avoid the Type 2. That said, I’ve worked with both extremes.

EDIT: When I say I’ve worked with both the extremes, I mean I have worked with both highly skilled and totally incompetent foreigners as well as natives.

EDIT 2: I’ve also worked with a third category — highly intelligent people (PhD level) who are more interested in spreading their intelligence (i.e. showing off) than getting actual work done. Unfortunately, I haven’t met the other extreme in this case. :-)