Vowing to fast every Monday: what should I do when I get ill?

I am not clear what you mean by "intended" because the relevant word in Arabic is used differently in different places. In some Muslim countries, the word is used to express an actual ‘vow’ which is referred to in Arabic as ‘nadhr’. This normally takes the form of a commitment to do something for God's sake.

A nadhr may or may not be connected to a particular event taking place. It is binding and must be performed unless the commitment is to do something forbidden. People normally make vows thinking that they are a means to achieve certain purposes but is not advisable to make them. It is much better to pray to God to fulfill our wishes and appeal to Him for help. In the Quran, we are advised to: "Ask God to give you out of His grace." We must remember that God the Almighty does not need our fasts, prayers, charity or any kind of worship. The devotional acts we perform are for our own benefit. We become better people because of the acts of worship we offer. Our devotional acts signify our firm belief in God, and He rewards us for our belief and compliance with His orders.

When a person makes a vow it must be fulfilled. If this is what you mean by your intention, then you must fast every Monday. When you cannot, because of an illness or your period, you are to compensate for it in the same way as you compensate for not fasting in Ramadan during your period. In other words, you must make up your fast on other days after you recover or finish your period. The fact that you do not make up your fast on a Monday is of no consequence, because your pledge is to fast. As for Ramadan, you do not need to compensate, because you will be fasting every Monday. If your nadhr commits you to fast every Monday for the rest of your life and you get old and physically unable to perform it, you must perform an alternative which comprises of giving food to a poor person in lieu of fasting.

On the other hand, the word "intended" may be taken in its Arabic meaning, which is a mere intention or directing one's mind to something, like when you say: "I aim to finish this task by 3 o'clock." In this case, you are not obliged to fulfill the intention. You can change your mind. As such, if you carry on with your intention, you do not need to compensate for not doing it at any time and for any reason.
And God the Almighty knows best.