Is it permissible to fast six or seven consecutive months to make up for missed Ramadan fasts during childhood, and does this fall under the prohibition of perpetual fasting?

It is recommended to make up for missed Ramadan (definition) fasts consecutively, based on the Almighty's saying: "And hasten to forgiveness from your Lord." The preponderant opinion is that consecutive making up is recommended, not obligatory. It is permissible to make up for them non-consecutively, based on the Almighty's saying: "then a number of other days." Fasting perpetually (fasting al-Dahr) does not fall under making up for Ramadan. It means continuous fasting every day, except for the two Eid days and the days of Tashreeq. The majority of scholars permit perpetual fasting for those who are able to do so and refrain from fasting on the prohibited days. However, the best is the fast of David (peace be upon him), who used to fast one day and break his fast one day. Making up for Ramadan after puberty is an obligation and a debt upon one's conscience, whereas what was before puberty does not require making up.