Strictly speaking no it would not be a risk. If it is a risk, it is a potential problem. If it is occurring throughout the project life-cycle, than it is an issue since the risk has already been realized.
With a risk, you can avoid it, mitigate it, accept it, or transfer it. Once it's an issue, you can not longer avoid it, so you're stuck with the other 3 options. Improve the situation, accept it, or make it someone else's problem. Saving Changes...
I understand your question that that risk event might occur at any time during the project and have an impact on project objectives at the time when it occurs. All risk strategies according to PMBoK ed6 apply.
For example it may rain and you get wet:
avoidance: stay inside
mitigation: take an umbrella, then you reduce the impact, not the probability
acceptance: just get wet
share: ask your partner to come with you and carry the umbrella
escalation: complain about the rain to your partner and let him/her solve the problem Saving Changes...
as Sergio has indicated, the duration of a risk remaining open is just one factor to consider when developing an appropriate response. For example, if the threat is very low impact and low probability, the appropriate response might be to accept it and monitor it on a watchlist.
Well duration does in fact play a part, not the most major part but a part nonetheless. If the projects is 99.99% complete, the duration plays a part for that risk; there isn't as much probability for the risk to occur as from the beginning of the project up until that time. Saving Changes...