You wouldn't be able to retrieve any item from the bag of holding while it is inside the antimagic field area of effect. After it leaves the field it will resume to function normally and none of its contents will be lost.
How does Antimagic field affect magic items?
Likewise, it prevents the functioning of any magic items or spells within its confines.
What does it mean?
An antimagic field suppresses any spell or magical effect used within, brought into, or cast into the area
Is there any other source that tells us what happens to a bag of holding when its magic is supressed? Yes, it is Dispell magic spell description.
If you succeed, all the item's magical properties are suppressed for 1d4 rounds, after which the item recovers its magical properties. A suppressed item becomes nonmagical for the duration of the effect. An interdimensional opening (such as a bag of holding) is temporarily closed.
In-game explanation for it is that bag of holding does not contain the objects in itself. It opens a portal to an extradimensional space where its "contents" is actually stored. In an antimagic field the portal stops functioning, just like portable hole or a teleportation circle would. But the antimagic field has no effect on the extradimensional space itself. Thus, objects stored in it remain intact and are accessible as soon as the portal is restored.
Other magical effects are suppressed too. It means they have no effect, but
Time spent within an antimagic field counts against the suppressed spell's duration.