There are only several things that they can cite as a reason of denial:
Sec. 209.2 Adjustment of status of alien granted asylum.
The provisions of this section shall be the sole and exclusive procedure for adjustment of status by an asylee admitted under section 208 of the Act whose application is based on his or her asylee status.
(a) Eligibility.
(1) Except as provided in paragraph (a)(2) of this section, the status of any alien who has been granted asylum in the United States may be adjusted by the director to that of an alien lawfully admitted for permanent residence, provided the alien: (Amended effective 7/6/98; 63 FR 30105)
(i) Applies for such adjustment;
(ii) Has been physically present in the United States for at least one year after having been granted asylum;
(iii) Continues to be a refugee within the meaning of section 101(a)(42) of the Act, or is the spouse or child of a refugee;
(iv) Has not been firmly resettled in any foreign country; and
(v) Is admissible to the United States as an immigrant under the Act at the time of examination for adjustment without regard to paragraphs (4), (5)(A), (5)(B), and (7)(A)(i) of section 212(a) of the Act, and (vi) has a refugee number available under section 201(a) of the Act.
Apart from criminal record, the easiest way for them to deny you is the change of COP conditions. Go figure.