With evictions in the post-birth world, we generally require some notice before the actual eviction. I have a hard time imagining that we would not do so for pre-birth evictions considering that the consequences to the evictee are much more severe.
Set that notice time to N months and you have then effectively prohibited abortions in the last N months of the pregnancy.
On the other hand, that may be pointless. If a landlord evicts someone without proper notice has the landlord committed a crime or just given the evictee a cause for civil action?
If it is just civil action then this approach wouldn't work for limiting late term abortions under evictionism because the injured party would be dead. Normally in the case of a dead pre-adult it would be up to the parents to sue, but since the mother would be the defendant she can't sue herself.
There is presumably a father though. If he didn't agree to the abortion maybe he could sue? That's a whole different can of worms in general--it takes two to create a pregnancy, so should both have a say in termination? If so what are the results when they cannot agree on whether or not to terminate?