Double negative not making sense

Question

From NHK Easy Japanese News:

「民主主義｛みんしゅしゅぎ｝は、一度｛いちど｝運動｛うんどう｝を止｛と｝めると、使｛つか｝わない筋肉｛きんにく｝のように弱｛よわ｝くなってしまうので、運動｛うんどう｝を続｛つづ｝けなければなりません」と言｛い｝いました。

If I translate literally:

"About democracy, if stop exercising once, becomes frail like unused muscle therefore, if don't continue exercising don't become," she said.

The last part, logically, seems to be backwards. I would expect either of

～運動を続けなかればなります。

～運動を続ければなりません。

Is the original sentence correct and so what is its meaning and why?

I am familiar with "must do" expressions using two potential negative forms like:

～なければいけません

But here the ending verb is simply なりません, not a potential form. Would this also express "must do"?

Answer 1

Yes, ～なければなりません also means the same as ～なければいけません. These two can be regarded as fixed phrases.

Therefore 運動を続けなければなりません means "they must continue the campaign."

It's enough if you understand this as a fixed phrase, but this can also be explained in a literal way:

The verb なる can mean "to succeed" or "to complete" as described in jisho.org and ～なければ means "if one doesn't ～".

So ～なければなりません can be interpreted as "if one doesn't ～, it's not ok".