This is based on a situation that's happening in my current campaign, though the example below is simplified to remove unnecessary context.
The shapechange spell (Player's Handbook, page 274) only limits the form that its user can change into by Challenge Rating, rather than size.
In the following situation, how, if at all, would shapechange be suppressed?
A level 20 wizard and a level 20 druid stand with 10 feet of space between them (figure 1).
To begin their battle, the druid casts shapechange, transforming into an ancient brass dragon, a Gargantuan creature (figure 2).
To counteract this, the wizard casts antimagic field (Player's Handbook, page 213) which creates a field of anti-magic in a 10-foot radius sphere around the wizard within
"Spells and other magical effects, except those created by an artifact or a deity, are suppressed in the sphere and can't protrude into it."
It seems clear-cut that shapechange is suppressed until the druid exits the antimagic field, and so reverts to its normal, medium form (figure 4).
Now the druid's smaller, Medium form, is no longer within the antimagic sphere. So it should regain the effects of shapechange, transforming back into an ancient brass dragon—which immediately puts its form back into the antimagic field, repeating the process. If it were another buff spell, such as fire shield (Player's Handbook, page 242), that doesn't affect the target's size, this would be a nonissue. But shapechange, along with enlarge/reduce (Player's Handbook, page 237), polymorph (Player's Handbook, page 266), and any other spell that might increase the target's size run into this issue.
Best Answer
If you maintain creature positions, the effect is simply suppressed and the druid remains in its typical form
The druid can't take the Brass Dragon form when some portion of that form would intersect the region affected by the anti-magic field. The order of events, as described in the question, is as follows:
I submit that there is a breakdown between steps 3 and 4. The effects of shape-changing spells are immediate and there is no time spent in the transformation (by RAW; cool narration may differ). So the transformations don't take up any time. But the Brass Dragon form cannot persist here, as the anti-magic effect prohibits it. Meanwhile the druid form can persist here.
Even if you favor an infinite loop of transforming back and forth, the druid cannot spend any time in dragon form here. But if time still passes, as over the course of a turn, the druid must have some form, and if it can't be the dragon it must be the druid. Therefore, as long as the larger, shapeshifted form would intersect the anti-magic field and immediately suppress the effect, the transformation cannot occur/cannot persist in time. The only form the druid can be in is one which does not enter the anti-magic field.
This is in line with a (somewhat but not exactly) analogous limitation described by Enlarge/Reduce:
You can only become as big as the space allows. The anti-magic is, in effect, a limitation on how large a creature could become. As shapechanging doesn't allow for dynamic sizing, the druid cannot be in its shapechanged form as long as the anti-magic effect would interfere.