minhag - Do we say "Ma Tovu" each time we enter the synagogue?

There is a custom to say the paragraph “מה טובו” on entering the synagogue (see “Avodah Shebelev” Rabbi A Z Sternbuch, 5753, page 18).

The idea (but without the possuk of “Ma Tovu”) is mentioned in Mishnah Berurah just before 46 [1]. Simon 46 is entitled 'הלכות ברכות השחר וכ‏‏‏. From the fact that it is mentioned in this Simon can I assume that it is only to be said in the morning when entering the synagogue, or should it be said every time one enters a synagogue?

Answer

Shulchan Aruch, Orach Chayim 151:1, discusses what one should do who needs to enter a synagogue not for prayer or similar purposes. It (and Mishna B'rura and Aruch Hashulchan there) do not say to say "Ma tovu".

Aruch Hashulchan 46:16 seems, a little more explicitly than the Mishna B'rura you cite, to restrict "Ma tovu" to shacharis:

The language of prayer before "Baruch sheamar" is printed in prayer books: When one enters the synagogue, he should say "Ma tovu", "Adon olam", …

Neither Mishna B'rura nor Aruch Hashulchan mentions "Ma tovu" when discussing what one says before mincha (MB 234:6–7; AHS 234:1–2,7) or maariv (MB 236:1, 237:2; AHS 237:1–2).