HI Varsha,
As per https://developer.salesforce.com/docs/atlas.en-us.api.meta/api/sforce_api_objects_account.htm can you IsPartner Indicates whether the account has at least one contact enabled to use the organization's partner portal (true) or not (false).

Can you alter your test class code to match the below and let me know if it works?

You need to Create User by Passing in the contact ID

Account a = new Account();
insert a;
Contact c = New Contact(LastName = 'Test', AccountID = a.id);
insert c;
User newUser = createPartnerUser(c.id);

private static user createPartnerUser(ID cId){
    Profile p = [Select ID, Name from Profile Where Name = 'YOUR PARTNER PROFILE NAME'];

    user u = New User(
        UserName = 'test_' + math.random() + '@test.com',
        FirstName = 'Test-First',
        LastName = 'Test-Last',
        Alias = 'test',
        email = 'test' + math.random() + '@test.com',
        CommunityNickName = string.valueOf(math.random()).substring(0,6),
        ProfileID = p.id,
        TimeZoneSidKey = 'America/New_York', 
        LocaleSidKey = 'en_US', 
        EmailEncodingKey = 'UTF-8', 
        LanguageLocaleKey = 'en_US',
        ContactID = cId

        );

    insert u;

    return u;


}

a = [Select isPartner From Account where ID = :a.id];
system.assert(a.isPartner,'Is Partner flag was not set to true');

Incase you have further queries, please post your narrowed code snippet so that I can take a look.

Thanks