Question
The buds at the end of the spray of orchids keep turning brown, and then shrivel up and die. The plant looks healthy apart from that, the flowers at the beginning of the sprays flower ok, but towards the end they don't. I only water and feed it once a week.

Answer
Thanks for your question Delia.  Watering and feeding is likely not a problem. I will assume that this orchid is newly purchased and hasn't flowered for you previously.  One possibility is that the terminal buds were exposed to cold while transferring the plant from the supplier to  your home. Buds are the most sensitive part of the plant and will be the first to respond to stressors such as cold.  It is also possible that the condition of the plant (including roots) is not strong or healthy enough to support the opening of all the buds.  When it has finished flowering, I suggest that you unpot your plant, wash off the roots and remove any dead, mushy roots before repotting in fresh orchid potting mix.  Plants can appear healthy but the potting mix may have degraded such that the root zone stays too wet and little air circulates through the potting mix.  Orchid potting mix is specially created to permit air flow to the roots and permits good drainage.  Also the pot should have good drainage with at least 6 holes in the bottom.

It is still possible that new buds can form on the old flower spike (this is not possible on all phalaenopsis) and form branches that flower.