Sustain means to hold up or bear up and support.  Just as we sustain Christ and his leaders on the earth today, they promise to sustain us.

Even if you cannot always see that silver lining on your clouds, God can, for He is the very source of the light you seek.  He does love you, and He knows your fears.  He hears your prayers.  He is your Heavenly Father, and surely He matches wit His own the tears His children shed . . . They (Heavenly Father and Jesus Christ) sustain us in our hour of need - and always will, even if we cannot recognize that intervention." Elder Holland

They are not leaving us without help.  We are being sustained all the while we sustain them.

"And whoso receiveth you, there I will be also, for I will go before your face. I will be on your right hand and on your left, and my Spirit shall be in your hearts, and mine angels round about you, to bear you up."  Doctrine and Covenants 84:88

We are never alone.  We may feel alone, but we are never alone.  No matter the situation He will always be by our side wanting to hold us up. 

Elder Holland also taught us that Christ walked the long and lonely road alone, so we don't have too.