Clearaudio Satisfy carbon tonearm front to back movement.

Sounds like you have the Satisfy Ten. Unfortunately the Satisfy Forever upgrade is very, very expensive. Since you can't hear it I say go with Plan A: 

may have always been there

My Conqueror does the same thing. Some bearings, in order to eliminate chatter or play use gravity. Doesn't take much in the way of handling to shift it. But they go back, gravity. Never even seen your arm. Haven't even searched. But if it sounds good and feels like that you can just about bet that's what it is.

@mgolpoor, How far is it moving in mm. 

If it is similar to the current Satisfy Kardan then it should not be loose at all.
Even a proper uni pivot should not move in that direction unless you pick it up off the pivot. Easy movement in that direction is very bad and indicates a bad bearing which is never good. The best tonearms move in only two directions, up and down, and side to side. Nothing else.
I would get a new arm but that is up to you. My worry would be record wear from bad bearings. I am also not an expert in that arm.

I’m not familiar with the Clearaudio pickup arm but no conventional pivoted arm should have that much play in the bearings. No good can come from it.

Unipivots are a little different but I admit a prejudice there - they just creep me out - even though I’ve heard some that sound fantastic, such as the VPI at Soundsmith.

@mijostyn........the movement is very slight.....my guess would be 1/4 to 1/2 mm.

@mgolpoor, That is enough. You have to understand that this is a vibration measuring machine. It is designed to read the waveform in the groove that is in the thousandths of mm. Fiction in the groove wants to pull the tonearm forward but the friction varies with the intensity of modulation (called groove velocity). With this variation the arm can move back and forth causing all kinds of distortion. Some bearings can be tightened. Some can not. Vertical bearings are easy, the screws will be on the side at the fulcrum. You move the arm back and forth with you left hand and turn the screw clockwise until the arm just stops moving. The horizontal bearing is more difficult. It is usually not adjustable. 
Basically, if you can't fix it it s new tonearm time. The Clearaudio Magnify is a great arm and should fit right in.

Cleeds and I agree that unipivot arms are bad news. They are inherently unstable which is not good for any cartridge but particularly the less compliant cartridges we use today. Some cartridge manufacturers like Lyra specifically recommend against them. 

I am not that familiar with clearaudio arms but i would say that the unipivot point has worn a bit and that is why you notice the slop or movement in the arm now after 10 years but this is my best guess.