I kind of agree with rendering it as 'the act of keeping in the mind'. B. Analayo proposes also 'presence of/in the mind'. But the former rendering has this drawback that the verb 'to keep' is transitive, so it calls for an object which is not present, as sati is an abstract concept that does not refer to a particular object (unless for example in anapanassati). So 'presence of/in the mind' seems to be a better rendering.
But there is a great difference in English between remembrance and awareness/mindfulness. If one is to hold on tenaciously to the former, the problem is that it may induce confusion for practitioners. Remembrance is directed to the present perception of a 'past object' (instructions for example), whereas awareness is directed to phenomena happening in the present moment.
The most advanced meditation teachers I know of all take sati in the sense of awareness/mindfulness. I don't see any reason to consider that they are all mistaken.