2:183 O you who believe, fasting has been decreed for you as it was decreed for those before you, perhaps you may be righteous.
2:184 A few number of days; however, if any of you is ill or traveling, then the same number from different days; and as for those who can do so but with difficulty, they may redeem by feeding the needy. And whoever does good voluntarily, then it is better for him. And if you fast it is better for you if you knew.
2:185 The month of Ramadhan, in which the Qur'an was revealed; as a guide to the people and a clarification of the guidance and the criterion. Therefore, whoever of you witnesses the month, then let him fast therein. And whoever is ill or traveling, then the same number from different days. God wants to bring you ease and not to bring you hardship; and so that you may complete the count, and glorify God for what He has guided you, that you may be thankful.
2:186 And if My servants ask you about Me, I am near answering the calls of those who call to Me. So let them respond to Me and believe in Me that they may be guided.
2:187 It has been made lawful for you during the night of fasting to approach your women sexually. They are a garment for you and you are a garment for them. God knows that you used to betray your souls so He has accepted your repentance, and forgiven you; now you may approach them and seek what God has written for you. And you may eat and drink until the white thread is distinct from the black thread of dawn; then you shall complete the fast until night; and do not approach them while you are devoted in the temples. These are God's boundaries, so do not transgress them. It is thus that God makes His revelations clear to the people that they may be righteous.
The only thing that could prevent one from observing fast is illness. The things which are prohibited is food, drink and sex during the time of the fast. We are not to have sex while we are devoted in the temples. I see no mention of menstruation.
2:222 And they ask you about menstruation? Say: "It is harmful, so retire yourselves sexually from the women during the menstruation, and do not approach them until they are cleansed. When they are cleansed, then you may approach them as God has commanded you." God loves the repenters and He loves the cleansed.
Note that the only prohibition during menstruation here is intercourse. There is no mention of either fasting or salah. Traditionally people say how can you fast or pray when you are unclean. The verse says you are unclean. What they fail to realise is that you are unclean for intercourse. I too am a bit uneasy with this, but this is what the verses say.
My wife has chosen to fast while menstruating an is fine, even while breastfeeding. She gets a lot of criticism from friends. I guess if a women generally experiences a painful difficult cycle then fasting may not be the best thing to do... make up for it later. If you are OK then fast.
May Allah forgive me for saying anything wrongly in His name, and may He guide us all