Phalaenopsis keeps producing basal keikis
 

I have a Phal Yu Pin Pearl that was given to me a while ago. The orchid was struggling and finally got healthy when a basal keiki appeared at the base. I let it mature and removed it. Both were doing great after repotting. To my surprise the mother plant produced another!! Then this morning it looks as if the 1st basal keiki has a basal keiki!!
I'm at a loss of whats going on. I water with reverse osmosis. I wasn't using any fertilizer. Is this normal?

There's really nothing abnormal about it. However, if it's not producing flowers as well it might be time to replace it.

Basal keikis are absolutely normal. Almost every mature Phal will get them sooner or later. How many/how often/how easy depends on the species background and the breeding, and sometimes the conditions. Leave the keikis attached and when you have a mature multi-crown plant with several spikes it will be quite impressive.

What is the time frame for all this? Can't really know if it should be flowering without knowing time and conditions. A healthy Phal can certainly grow keikis and flower at the same time.

Question one: Is the crown of the "mother plant" intact? If not, that explains the keikies. However, while the production of basal kekies is not unusual, if that's all the plants do, it's certainly not normal.

It may be that you have a genetic odd-ball - the remnant of over-cloning, perhaps - but we cannot overlook culture.

You stated that you use RO water and don't fertilize. That is the best way I know to starve your plants. If you give the plant just a little food, it will go a long way to helping it bloom. It may not resolve the keiki situation, but if it blooms, who cares?

Don't misunderstand: fertilizer does not cause blooming, but starvation certainly can prevent it.