Peeling bark is not always cause for concern. For instance, the crabapple variety 'Brandywine' has beautiful exfoliating bark that is natural to the tree and one of its nicest features. Most crabapples develop a 'mottled' looking bark as they mature.

If you see bark covering wood after older bark peels away, the tree is naturally exfoliating. However, if you see bare wood under the flaking, then there is a different cause; either environmental or disease.

Bark damage can occur from wintertime problems. Frost crack and sunscald are common injuries. The best thing you can do for young trees in the winter are keep them watered when it is dry, and wrap the trunks for the first several years. Always removed the tree wrap in the spring. A good rule of thumb: wrap by Thanksgiving, unwrap at Easter. Here is a link with more information:

http://extension.colostate.edu/topic-areas/yard-garden/environmental-disorders-of-woody-plants-2-932...

Another cause of bark peeling on crabapples is a disease known as fireblight. This is a bacterial disease that occurs in when spring weather is warm and rainy. Some leaves will wilt, then will eventually turn black. The bark on the trunk or branches may be cracked or peeling. Here is a link with more information:

http://planttalk.colostate.edu/topics/insects-diseases/1411-fireblight/

A common cause of bark problems is wildlife damage, such as deer or squirrels. They will strip and eat the bark of crabapple trees. Here is a link with more information:

http://planttalk.colostate.edu/topics/wildlife-issues/2303-squirrel-damage-trees/

Does the tree look healthy overall, and flower and/or bear fruit? It is difficult to determine what's happening in this situation. Photos are really needed in order to see what exactly the flaking bark looks like. Otherwise, we can only provide you with possibilities of what may be occurring.

No, don't wrap the tree year-round, only late Oct-mid April, for the first several winters on site.

It looks like deer or voles may have damaged the lower trunk.   Severe cold snap of Nov 2014 may have damaged that bark, killing it in places, now sloughing off to exposed wood below.  In any case, this crabapple now has less water-conductive inner bark, so it's a bit stressed.   There are a few areas of bark discoloration (black cankers) above the main "wound". 

This crabapple may show some die back this summer or next spring.  Try to keep it healthy with sufficient but not excessive watering.   Water during dry warm spells in winter months.