Schengen travel insurance for 3 entries

This would seem to depend on your insurer. Some travel insurances are “per trip”, defined as the time spent out of your country of residence and expire when your return there. Others have a specific length of time and cover several trips during that period. Both variants would seem to cover your trip but there might be others I don't know about.

As far as Schengen regulations are concerned, you need to prove you are covered each time you apply for a visa. If you apply for a multiple-entry visa, it's enough to show that you are covered for the first trip you plan and to get insurance for subsequent trips later on.

Here are the relevant bits from article 15 of the Schengen Visa Code:

1. Applicants for a uniform visa for one or two entries shall prove that they are in possession of adequate and valid travel medical insurance to cover any expenses which might arise in connection with repatriation for medical reasons, urgent medical attention and/or emergency hospital treatment or death, during their stay(s) on the territory of the Member States.

2. Applicants for a uniform visa for more than two entries (multiple entries) shall prove that they are in possession of adequate and valid travel medical insurance covering the period of their first intended visit.

   In addition, such applicants shall sign the statement, set out in the application form, declaring that they are aware of the need to be in possession of travel medical insurance for subsequent stays.