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Set sufficient value of processes/sessions in init/spfile of database , might be session limit of DB is getting exceeded & restricting new connection.
Check alert log & below query o/p , CURRENT_UTILIZATION < MAX_UTILIZATION to get connection to DB
Also , try to connect as sqlplus prelim & do hang analyze , refer below link
select * from v$resource_limit;
sqlplus -prelim "/as sysdba" ORADEBUG HANGANALYZE 3