The procedural problem is easy to state and has resisted forty years of attempts to solve it.
Ordaining a bhikkhuni requires a quorum of existing bhikkhunis, together with bhikkhus. The Theravada line lapsed, in Sri Lanka in the eleventh century, in Burma at about the same period, and once it lapsed there were no bhikkhunis to form the quorum. The requirement had eaten itself.
For eight centuries the consequence was that women in Theravada countries lived as maechi in Thailand or thilashin in Myanmar: shaven, robed, keeping eight or ten precepts, and not ordained. The gap is not merely one of status. It carries access to monastic education, to state support given to the sangha, to legal recognition, and to the alms economy that sustains monks.
The revival, and what is disputed about it
Ordinations were performed at Sarnath in 1996 and at Bodh Gaya in 1998, using bhikkhunis from the East Asian Dharmaguptaka lineage, which never broke, alongside Theravada bhikkhus. Several thousand women have since been ordained on that basis. In Sri Lanka the revival has broad support and the bhikkhuni order is functioning.
The Thai and Burmese hierarchies do not accept it. The objection is that a Dharmaguptaka quorum cannot validly ordain into the Theravada order, the two following different Vinaya recensions. The answer offered is that the Vinaya lineages descend from a common origin and that the Chinese order was itself founded by Sri Lankan nuns in the fifth century, which makes the borrowing a return. Neither side has a body above it that could rule.
The Thai supreme patriarch's order of 1928 forbidding monks to ordain women has never been rescinded, so Thai women seeking ordination have gone to Sri Lanka. In 2009 Ajahn Brahm took part in a bhikkhuni ordination at Perth and his monastery was expelled from the Wat Pah Pong lineage for it, the clearest available marker of how the disagreement is enforced, which is by exclusion rather than by argument.
Tibetan Buddhism has the same problem and has not resolved it either. The Dalai Lama has said repeatedly that he supports full ordination for women and that he cannot decide it alone, since the decision belongs to an assembly of Vinaya holders that has not reached agreement.