Dimensional Anchor (spell): "Any creature or object struck by the ray is covered with a shimmering emerald field that completely blocks extradimensional travel."
It doesn't list those forced movements in the examples, but in the examples it said, "including" meaning it's not limited to those examples (which were really just spells that weren't explicitly extra-dimensional, save for gate, I believe). It makes sense - just as sailors use physical anchors to prevent unwanted sea travel, so too can an extra dimensional being use a dimensional anchor to prevent unwanted dimensional travel.
You would have to see the banishments coming. Of course, you could get some type of auto-casting equipment...ring of counter spells? Countering the spell could work, but not quite what I meant...I can't think of anything else that would cast Dimensional Anchor on yourself, in response to being targeted by banishments. Perhaps you could finagle a custom magic item that is continuous to cast it on you when targeted? Ask your GM.
Of course an even more general way to defend against it is to have a really high will save. Many magic items do this on the relatively cheap. Barbarians can also rage, gaining will save. For a one level dip, and the feat to turn raging into an immediate action (allowing you to interrupt an action to rage, gaining the bonuses before it strikes), you would have a bit more protection. Of course, this protection is equivalent to Iron Will...but there are side benefits to the immediate rage other than the will bonus.