Sovereign Glue is a magic item that permanently bonds two objects together. However, magic items stop working in an antimagic field. So, if you put two objects, bonded by Sovereign Glue in an antimagic field, would the objects cease to be bonded?
The bond is retained.
The description of Sovereign Glue says (emphasis mine):
Wondrous item, legendary
This viscous, milky-white substance can form a permanent adhesive bond between any two objects. It must be stored in a jar or flask that has been coated inside with oil of slipperiness. When found, a container contains 1d6 + 1 ounces. One ounce of the glue can cover a 1-foot square surface.
The glue takes 1 minute to set. Once it has done so, the bond it creates can be broken only by the application of universal solvent or oil of etherealness, or with a Wish spell. (DMG p.200)
Given the highlighted phrases, the bond itself is not magical and can only be broken by the given methods. The three listed methods suggest that they dissolve/remove the glue bond, not dispel magic.
- Universal Solvent and Oil of Etherealness are both Legendary items, and a Wish is a level 9 spell.
- It is listed as a magic item, so you probably would not be able to apply the glue in an anti-magic field.
There's a checklist
It's often impossible to tell if a thing is magical or not, which matters a lot when adjudicating dispel magic, antimagic field, and similar effects. As a result, Wizards released a checklist in the Sage Advice Compendium which can be used to determine this sort of thing. Essentially, things are only magical iff it elicits a 'yes' result from one of the following questions:
Is it a magic item?
Is it a spell? Or does it let you create the effects of a spell that’s mentioned in its description?
Is it a spell attack?
Is it fueled by the use of spell slots?
Does its description say it’s magical?
It's still unclear, though
While the glue itself is clearly magical, what matters is whether or not the bond the glue creates is magical, since that's what antimagic field would be affecting. That bond isn't called out as magical and doesn't use spell slots and isn't a spell attack and is neither a spell nor a spell-like ability, but it might itself be a magic item.
If you rule that the bond created by sovereign glue is itself a magic item, then the bonding would be suppressed by an antimagic field, but this would be largely irrelevant since the bond is certainly created by magic so if it is an item then it also would "temporarily [wink] out of existence". This can be complicated to adjudicate; what I do is have the part where the two surfaces are joined temporarily fold out of the universe so people can't tell where one ends and the other begins, which also means that the objects remain functionally inseparable since the joining, though no longer magically protected, also no longer exists.
If you rule that the bond created by the glue is not itself a magic item and furthermore not an item at all, then it's not affected by the field and would continue being just an inseparable as ever.