Ir or irse or neither?

For your sentence 'I may be going away on that day' a correct translation using "ir" in the subjunctive mood would be "Puede que yo vaya ese día". Here, "Puede" is the present indicative form of "poder", and "vaya" is the present subjunctive form of "ir". The subjunctive is used because it expresses a possibility or a hypothetical situation.

If you want to use "irse" which emphasizes the action of leaving, the sentence would be "Puede que yo me vaya ese día", using "me vaya" as the present subjunctive form of "irse".

The choice between "ir" and "irse" depends on whether you want to emphasize the action of leaving or just the general act of going.