It is not a problem, some Phalaenopsis will bloom for years.
It is only a "problem" if you join an orchid society and wish to show your blooms. Orchid judging standards will vary from country to country but the number of blooms and the appearance of the flowers on the flowering stem are taken into account. You would still get some points for benching your plant.
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These are not my orchids, I know the owners, they cut the flowering stems down to the base once the flowers start to decline.

This post was edited by arthurm on Fri, Nov 29, 13 at 15:45

From my experience with a Phal that was in constant bloom for over 2 years, I'd cut the stems off.
It was a very strong growing French hybrid. to begin with it was a very pleasing plant with large red spotted white blossoms. After over 2 years it looked very scraggly with the blossoms on long zig-zag stems.
But, worst of all, it seemed to collapse from exhaustion. The plant itself [leaves] looked terrible. It threw off a keiki and then died. The keiki did fine. I never let it bloom for that long of a time period. I had several other Phals that did not have any problems while being grown right along side that one. Cutting the stems off will not harm the plant. It will bloom again the following year.

This post was edited by solo_voyager on Sun, Dec 1, 13 at 13:05

I have pretty good luck with the 1/2 price and $5 orchids from Walmart. They bloom and bloom. I have a question. The keiki is it a small plant on a stalk? I have one and wonder what to do with it. The plant is blooming so I have left it alone for a year. it is getting big and bending the stalk down.

I would cut those spikes back and let the plant put energy into new spikes. I do that with great success

I hve one that has bloomed since 2019 and keeps putting of spikes on spikes with blooms