Although Sheila Carter has managed to trap Eric Forrester into marrying her, their marriage was doomed from the start
For starters, Sheila, who claimed to deeply love Eric was very insensitive to his feelings and moods. She saw sex as a remedy to everything. That's why for instance when Eric was very agitated and on the verge of having a heart attack when he lost control over Forrester Creations to Brooke, all his "loving & supporting" wife Sheila had to offer was a seduction in the hot tub.
Sheila's insensitivity wasn't the only problem. Lauren Fenmore and Mike Guthrie were hovering in the background threatening to reveal Sheila's crimes to Eric. And if that wasn't enough, there came Brooke Logan Forrester and as her first move as Forrester creation's CEO appointed Sheila as her liaison to the Forresters.
Sheila's siding with Brooke infuriated the Forresters and drove Eric to demand a divorce because he felt he could no longer trust her. But Sheila convinced him to give her another chance and go on a romantic vacation to Catalina Island.
On Catalina, Eric & Sheila ran into Lauren and the dying Scott Grainger. Lauren was kept from telling Eric the truth by Scott's dying wish. And clueless Eric, who wrongly perceived Sheila's grief over Scott's death as a compassion for a dying stranger, was so touched by it that he canceled the divorce.
Although there was no more talk about a divorce, Sheila was very insecure especially about Stephanie as a threat to the marriage. Her growing insecurities made Sheila very unattractive to Eric and he suspended their love life until she will stop resenting Stephanie.
Eric had a golden opportunity to get rid of Sheila, when she offered to let him go if that's what he truly wanted. But Eric, being his compassionate (and very stupid if you ask me) self was again touched by the offer and declined.
The truth is that Eric wasn't emotionally strong enough to go through yet another divorce so soon after the very painful divorce from Brooke. That's why Eric had a vasectomy without telling Sheila, when he realized that she will do anything to have his baby.
By that time the marriage was already doomed. Desperate Sheila wanted Eric's baby as a meal ticket after she stole and read his will. And when Eric told her to forget it she went as far as trying to get pregnant by Connor Davis.
As much as he didn't want it, Eric was finished with Sheila when during a quarrel she lied and told him that she was pregnant. Eric snapped back that the baby couldn't be his because of the vasectomy and ended the marriage.