Many contracts have automatic renewals or specific procedures that must be followed to prevent auto renewal.  Some take it for granted that dates negotiated on their last RFP made it into the contract, this is often not so.  Always check your contracts and know the procedures, dates, and revenue commitments agreed upon.

Some jump the gun and turn the incumbent provider into an enemy before knowing the particulars of how to discontinue their agreement.  It is also important to consider the time and resources necessary to move to another provider.  Know your dates and plan in advance.  Staying one step ahead of your providers will help you to negotiate the best deals.

Usually, TEMs are viewed as providing a very short term engagement, where they reduce costs quickly.  TLMs are expected to provide a holistic view which might begin at expense management but would also look at order fulfillment, asset management, managing SLAs, and on and on.  But is it unrealistic to expect long-term savings from short-term engagements?  No.  Any TEM/TLM should be able to provide recommendations for extended savings.  The biggest obstacle to maintaining and increasing savings is your organization.  Loss of efficiency usually takes place when there is no communications between people negotiating contracts and people ordering services, and when there are no quality management processes in place to monitor activity (MACD, Contract maturity, organizational changes).

TLM is something that you should be getting from any vendor, but it is only achievable with buy-in from your organization.  Monitoring processes from cradle-to-grave is the only way to achieve long-term savings.