Students should be facilitated to access on-line support.
Students should be facilitated in accessing on-line support.
Staff should facilitate students to access on-line support.
None of the sentences are, in my view, grammatical.
But you could say "The staff should facilitate access to on-line support for students". It is not the "students" who are being facilitated, but "access for students". You can facilitate a process, an event, an action, or a result etc., but you cannot, in my opinion facilitate a person.
But "enable" works differently. You could say "The staff should enable students to access on-line support". It is a more versatile word, because you could also "enable access for students".
The staff should facilitate students in accessing the on-line support.
Mods, can we rephrase the sentence for enhancement?
Students should be provided with the facility of accessing the on-line support.
Staff should facilitate students' access to online support.
You can avoid the issue entirely and make the statement clearer and shorter by recasting the sentence: --Students should be able to access online support. --Students should be helped to access online support. --Staff should help students access online support.
I think students should be 'enabled' to do something in the future. I also think that staff should help facilitate a student's access to on-line support. However, I would hope that the students were facilitated to do something in the past.
Facilitated is the past participle, so its use to describe a future event is incorrect.