As Weiss 2009/2011 mentions, word-final –e is “normally retained” (p. 147; emphasis mine – Alex B.). That being said, there are some few cases when word-final –e was lost (or apocopated).
In your question, you ask us specifically about imperatives from compound verbs of dico, duco, and facio. In my answer below I will address this issue only. If you are interested in imperatives of simplex dico, duco, facio, and fere; how to interpret data from Archaic Latin (Plautus and other authors) – it’s not that simple as Draconis has been trying to convince us here – I am willing to write a separate answer, just post another question.
Now, revenons à nos moutons.
First, facio. Based on whether the root vowel is changed or not, the derivatives of facio can be grouped into two classes:
Type A. calefacio [root vowel preserved], compound verbs (two roots).
Type B. conficio [root vowel weakened], prefixed verbs.
However, the 2nd singular imperative of both types is formed the same way: calface! confice! areface!
Secondly, dico. Weiss argues that compound 2nd singular imperatives from dico are not attested in Classical Latin.
Finally, duco and fere. Apocopated forms are standard in Classical Latin:
Apocopated means that originally they had –e at the end (in fact, such forms are attested) but eventually it was lost. Note that there are no root vowel changes in these compounds. Another strong evidence in support of this analysis comes from accentology. Such apocopated singular imperatives are oxytones, i.e. the last syllable is stressed:
The most interesting question that has not been addressed in the other answers – even though you clearly ask us – is how we know when the root vowel changes or not.
Weiss discusses it on pp. 121-122 (footnote 25, citing Garrett 2005 and Pultrova 2006).
Back root vowel [no change in compounds]: duco – adduco, educo etc. and, respectively, adduc, educ etc.
More diverse morphology [vowel weakening, a changes to i]: facio – conficio and its 2 sg. imperative confice.
Imperatives from compounds of duco and fero: short (apocopated) forms, e.g. educ! effer!
Imperatives from compounds of dico: not attested in Classical Latin
Imperatives from compounds of facio: unapocopated forms, e.g. calface! confice!