Tensed verb form or the plain form when used after "that" (in a mandative construction)

The issue in your example is not with each, but with the verb recommend. This keep is in the present subjunctive, which can be used after a main verb that expresses a command or recommendation (though not after all such main verbs):

She suggested that he stay away from the palace.

They recommend that the mayor should step down.

You can use either should or the present subjunctive. Some people also (sometimes) use the simple indicative (keeps, stays, steps), but this is considered ugly or illiterate by others.

• The tour guide recommends that each child keep close to his or her parents in order to avoid leaving someone behind.

Your example is in the form of a subjunctive mandative construction, which is seen in the use of "keep".

The example could, instead, use "keeps" or use "should keep", in which case the constructions would be covert-mandative and should-mandative, respectively.

For instance: the subjunctive mandative,

• The tour guide recommends [that each child keep close to his or her parents in order to avoid leaving someone behind].

the should-mandative,

• The tour guide recommends [that each child should keep close to his or her parents in order to avoid leaving someone behind].

the covert-mandative,

• The tour guide recommends [that each child keeps close to his or her parents in order to avoid leaving someone behind].

Many times, for some speakers, there are differences in preference as to type of construction.

Mandatives involve deontic modality, so those three types of mandative basically mean the same thing. But there can often be examples which could be ambiguous as to whether it is a mandative or a non-mandative, and thus, ambiguity in the meaning. For instance, the following example (borrowed from CGEL, page 996),

• [8.iii] She insists [that he takes / they take the eight o'clock train].

The version using "he takes" could be a covert-mandative, and the version using "they take" could be a covert or a subjunctive mandative; but both versions could also be non-mandatives. In the mandative interpretations: she insists on his (them) taking this train. In the non-mandative interpretations: she asserts that it is a fact that he (they) is scheduled to take this train.

(Reference: The 2002 reference grammar by Huddleston and Pullum et al., The Cambridge Grammar of the English Language, "7.1.1. The mandative construction", pages 995-1000.)