I don't know much about HOA's, so maybe someone else can answer on that.  I didn't know one could be dissolved - especially if your deeds say you must be a member.  But if you did dissolve it, I would think road maintenance would have to be provided by a road association of some sort, the difference being that a homeowners' association can do things not related to road maintenance, (grounds maintenance etc.,) where a road association is only concerned with maintenance of the road.  

You say there are only three properties, so you cannot form a statutory road association under 23 MRS section 3101-3104, which require at least 4 benefited properties.  You could still use those statutes as a guideline for how to proceed, which would assure that you are providing due process and that you have some structural guidelines.  However, you could not claim to actually be a statutory road association, and therefore you would not have the liability protection or the enforcement powers of a statutory road association.

Your other choices for road maintenance would be either an informal or voluntary association, where each person chips in on the cost but there is no means to force them to pay, or one person can just take over road maintenance and hope the others will pitch in on the cost. 

One other option would be to try to use 23 MRS section 3121, which says that when more than one residential property shares a common benefit from a private road, if there is no road association or road maintenance agreement it's assumed they each share equally in the cost of maintenance.  That statute provides no structure or due process, which is why I would advise using 3101-3104 as a guideline anyway.  Section 3121 does provide some enforcement power by giving one landowner the right to sue another who does not pay.  But that's not a great way to maintain friendly relations with your neighbors! 

The route you  decide to go may depend partly on why the HOA is dissolving.  Is it because everyone agrees you don't need anything beyond road maintenance, or is it because the three landowners cannot agree?  If the three of you get along, I'm sure you can work out a way to share the cost so your access remains passable for all of you.  If you don't get along, trying to force compliance by any means will likely be met with resistance.

Here are links to the statutes I mentioned:

https://legislature.maine.gov/legis/statutes/23/title23sec3101.html

https://legislature.maine.gov/legis/statutes/23/title23sec3121.html