General synonyms:
* Lasting
* Enduring
* Permanent
* Continuing
* Persistent
* Everlasting
* Unchanging
* Unwavering
* Stable
* Firm
Synonyms emphasizing a strong emotional connection:
* Deep
* Strong
* Unflinching
* Unbreakable
* Unyielding
* Devoted
Synonyms emphasizing persistence:
* Relentless
* Unrelenting
* Tenacious
Synonyms emphasizing agreement or acceptance:
* Accepting
* Tolerant
* Compliant
The best synonym for "abiding" depends on the specific meaning you want to convey. For example, "lasting" would be a good synonym if you're talking about something that continues for a long time, while "unwavering" would be a better choice if you're talking about a belief or commitment that is never shaken.