Is a woman permitted to seek divorce from her husband who has repeatedly committed adultery, after she had previously given him a chance and he promised repentance, especially since she now feels intense loathing towards him and is experiencing psychological pressure that has brought her to the verge of collapse?

Advise your husband and call him to repentance, reminding him of Allah's punishment and death, while treating him kindly and encouraging him to associate with righteous people and attend circles of knowledge. Also, supplicate for his guidance. If he does not straighten up, then you have the right to seek a divorce, while weighing the pros and cons and choosing the lesser of two evils. If you find that your staying with him is the lesser harm, then there is no blame upon you, and focus on raising your children, for Allah does not let the reward of the good-doers be lost.