SQL Server 2012 - Know when a SEQUENCE has recycled or is nearing cycle phase
There is no metadata view that is going to clearly give you this information. Your best bet would be to have a scheduled process that runs every few minutes and looks at sys.sequences and evaluates if the current_value is less than the prior current_value, in which case you would know that it had cycled. 

You can also compare the current_value to the maximum_value to see how close you are to hitting the cycle point.

A very basic view of this would be the following with a small sequence, you can see the initial values remaining, what it looks like after using a few sequences, and then how it gets reset as the sequence cycles.

CREATE SEQUENCE dbo.TestSeq 
AS SMALLINT
MINVALUE 1
MAXVALUE 10
START WITH 1
INCREMENT BY 1
CYCLE;

SELECT  name ,
        current_value ,
        maximum_value ,
        CAST(maximum_value AS BIGINT) - CAST(current_value AS BIGINT) AS Values_Remaining
FROM    sys.sequences
WHERE   name = 'TestSeq';
GO

SELECT NEXT VALUE FOR dbo.TestSeq;
GO 5

SELECT  name ,
        current_value ,
        maximum_value ,
        CAST(maximum_value AS BIGINT) - CAST(current_value AS BIGINT) AS Values_Remaining
FROM    sys.sequences
WHERE   name = 'TestSeq';
GO

SELECT NEXT VALUE FOR dbo.TestSeq;
GO 6

SELECT  name ,
        current_value ,
        maximum_value ,
        CAST(maximum_value AS BIGINT) - CAST(current_value AS BIGINT) AS Values_Remaining
FROM    sys.sequences
WHERE   name = 'TestSeq';
GO