Is it permissible to continue a romantic relationship (love and flirtation) with a married woman, even if she is in the process of separation, with the intention of marrying her after her divorce, knowing that there have been failed attempts to cut off this communication?

You must cut off relations with the woman and not be lenient in speaking to her or corresponding with her without a legitimate need. This applies even if the conversation is about religious matters and cooperation in good deeds, for all of that is a deception of Satan. You must fear Allah and not make excuses about fearing for her, for Allah is more deserving of fear and piety. If the woman has separated from her husband and her waiting period has ended, there is no harm in marrying her.