Time words + be +  Repeating the time words 

This construction is not commonly used, however you can still hear it sometimes. This "be" is foreign grammar element that comes to between the time words and it can give the meaning of "gradually  decreasing or increasing -----  improving or worsening " . or  " regularly = from month to month = aybeay  , or each moment = anbean 

note : it is written as "one word" 

an + be + an ==> moment by moment 

Anbean sağlık durumu kötüleşiyor. ----> His/Her  health situation is getting worse moment by moment.

-------------------------------------------------------

Bu sokak anbean kamerayla gözetleniyor. ----> This street is being watched each moment by a camera.

-------------------------------------------------------

gün +  be +  gün ---->  day by day 

Günbegün Türkçem iyileşiyor. ----> Day by day my Turkish is getting better.

--------------------------------------------------------

ay + be + ay ----> every month 

Borcumu aybeay ödüyorum. -----> I am paying my debt each month. [regularly]

I think this "be" is Farsi "ber". It means "on" So we say day on day instead of day by day

I think we can also use günden güne for day by day. 

Kar günbegün eriyor.

Kar günden güne eriyor.