Why do Classical CDs sound less Alive/Real/Present ?

a lot of instruments going on at one time?

It's true, and modern classical production uses multiple microphones that are placed close to the instruments. The result is the entire orchestra recorded at full volume with no sense of space between instruments and no ambient sound.
Classical music (and jazz) in days past were recorded using minimal mic's strategically placed to pick up the sound of each section of the orchestra; eg, one mic for the brass section. The mic has a pickup pattern which is shaped liked a hemisphere and can pick up sound from the front as well as left and right side. This technique of mic'ing provides space and dimension between instruments.
There are also microphones placed high above the conductor and across the front of the stage to pick up the natural ambience of the concert hall. When the performance is mixed, there is a live feel to the recording. The soundstage has dimension rather than a flat close up sound.

Try sampling some stereo performances from the 1960s to early 70s. There are certain record labels such as Telarc who have always used the best recording techniques.

Or maybe you're not getting proper imaging due to the positioning of your speakers or room treatments. 
Too much absorbion on the wall behind the speakers will flatten the image, IOW there won't be any 3D presentation.
Try moving your speakers forward or farther apart. Maybe they need toe-in. 
My room is 12' x 16' and I listen to classical CDs. My digital playback presents symphonic music as realistic, spacious, and dynamic. Of course, some CDs sound terrible, and if the performers are over-mic'd the music will sound flat and congested.

Can you tell us about your system?

Some classical recordings are really bad -- shrill violins, and not very natural in general. However, some can be quite good. Try a few recordings on the BIS label, especially those with Ingo Petry as the recording engineer or producer. (He is a genius.) I’ll be surprised if they sound like you’re using a lesser grade of equipment.

The BIS recordings don’t always sound like an orchestra in a hall -- there is some spotlighting -- but to my ears they sound clean, clear, and well balanced, with natural timbres.  There are also good recordings from the 1950s and 1960s but the modern BIS versions, being all digital, have better pitch stability, among other things.

I recommend the classical recordings made by Donald Fine (Mercury Living Presence) using just one mic above the conductor. So the sound captured is what he heard. I like this better than the multi-miked approach - though good recordings (RCA Living Stereo) can result. London/Decca's mike "tree" was used quite successfully with Solti's Ring - a landmark recording!

Get some of the Mercury Living Presence CDs mastered by Wilma Fine! Far more natural sounding than the typical Columbia and Deutsche Grammaphone multi-miked affairs!