Praying During Menstruation

First, we must be aware that the salat (prayer) is an act of worship.
The menstruation is a bodily correction and function that is not any different from other bodily functions such as prespiration or excretion. There is nothing evil or sinister about bodily functions, after all they are God’s design. There is no reason whatsoever that should stop us from worshipping our Creator when our body's are performing one of their functions? The only Quranic prohibition related to menstruation is that married couples should not have sexual intercourse during menstruation, but they should never stop worshipping God.

More important, those who prohibit things which are not prohibited by God are are in fact rejecting the Quran, and thus they are disbelievers. The believers should never prohibit something that is not prohibited by God in the Quran. The following Quranic words confirm this issue:

[6:150] Say, "Bring your witnesses who would testify that God has prohibited this or that." If they testify, do not testify with them. Nor shall you follow the opinions of those who reject our revelations, and those who disbelieve in the Hereafter, and those who stray away from their Lord.

Also, the following ayat (verse) confirms that we should never follow any rules/laws not decreed by Allah Himself:

[42:21] They follow idols who decree for them religious laws never authorized by God. If it were not for the predetermined decision, they would have been judged immediately. Indeed, the transgressors have incurred a painful retribution.

The only source for God's law is the Quran and nothing else:

[6:114] Shall I seek other than God as a source of law, when He has revealed to you this book fully detailed?

If anyone tells you that the prophet prohibited women from observing salat during menstruation, do not believe them! The prophet was commanded to deliver God's message but he was not allowed to prohibit anything that is not prohibited by God. We have the proof of this in the Quran. If any hadith claims that the prophet made such a prohibition then it is false and is a lie against the prophet.
Once, the prophet Muhammad made an error of prohibiting something that was not prohibited by God, and immediately God reprimanded him:

[66:1] O you prophet, why do you prohibit what God has made lawful for you, just to please your wives? God is Forgiver, Merciful.

God deliberately included this verse in the Quran, not to belittle the prophet, but to make the fact known to all people and at all times that the prophet does not have the authority to prohibit what God did not prohibit, and that the only Law Giver is God Himself (6:114).