Why can't hemineglect patients be trained to actively pay attention to their neglected side? I'm still having a hard time understanding the symptoms of hemineglect, mainly because perception and attention has been two peas of a pod for most of my experiences.

A Scholarpedia article states that a hemineglect patient is likely to shave just one side of their facial hair (thus having left half of their beard intact).

I also know that while hemineglect patients have harder time attending to the side contralateral to the lesion location, external effort to bring attention to the contralateral side can bring attention to the contralateral side temporarily.

If that is the case and the patient is still familiar with the concept of body symmetry, then my question is:

Why doesn't the patient use their concept of symmetry to force themselves to pay attention to the contralateral side? 

Is even the concept of bilateral symmetry affected, possibly because any memory of an object brought up from long-term memory also loses the contralateral side?
Short answer
Symptoms of hemi-neglect are often accompanied by additional layers of cognitive deficits that make rehabilitation challenging. Logic reason is often dissociated from these patients' perceptions, or they simply dismiss there is a problem altogether.

Background
Hemineglect is the impaired or lost ability to react to, or process sensory stimuli presented in the hemispace contralateral to a lesion of the human right or left cerebral hemisphere. Besides this sensory neglect, motor neglect may occur, manifesting itself as a reduced use or even non-use of a contralateral extremity. Finally, there is representational neglect, referring to impaired spatial imagination (Kerkhoff, 2001).

In terms of rehabilitation treatment of neglect, it seems indeed logical to suggest the patient to actively start paying attention to the neglected side in tasks of everyday life. In fact, this is an accepted rehab strategy used, which can be regarded as a coping strategy. Though this approach is intuitively the most straightforward way to rehab these patients, it often proves to be difficult for therapists, because often additional, more global cognitive deficits exist besides the hemi-inattention (Marshall, 2009). As you indicate, anosognosia (deficit of self-awareness, i.e., a disability to acknowledge the existence of his or her disability) is seen in hemineglect patients in up to 20% to 58% of cases. When the patient dismisses the problem, treatment is next to impossible. Personality changes such as apathy, emotional instability, disinhibition and agitation further complicate rehab. Finally, although perception may be abnormal, and it can be pointed out to them (e.g., 'this arm that you claim is not yours can be traced back to your body), they are often unable to reconcile logic of the situation with abnormal perceptions. An example is given by Marsshall (2009), where a patient is described who reported that his hospital room was the “only one to have telephones with 2 columns of numbers.” On a line bisection task, a hemineglect patient may be trained to move the gaze leftward to identify a cue at the left extent of a line, confirming that the whole line is in view, and yet, that patient may still bisect the line to the right of midpoint as the gaze tracks rightward. 

Hence, there is a dissociation between perception and logic. This was examplified by Ramachandran et al. (1999). They investigated twelve patients with left hemineglect caused by right hemisphere stroke by showing them a mirror. A mirror was placed on their right side (their 'good'side), while 
an object was held out for them on their left (their neglected side). The patients were made explicitly aware that the object was on their left and that the mirror was just a reflection of the object. And still, a substantial
subset of patients (no numbers are provided in the article, unfortunately; it is a pilot-report) repeatedly reached for the object’s reflection on the right, even going so far as to say, “it’s behind the mirror.” 

Thus, brain injury may result in more that just a hemi-inattention. Other cognitive deficits add to the complexity to the syndrome and pose challenges to devise effective rehab treatments (Marsshall, 2009).

References
- Kerkhoff, Prog Neurobiol (2001); 63(1): 1–27
- Marshall, The Neurologist (2009); 15(4): 185-92
- Ramachandran, Med Hypotheses (1999); 52(4): 303-5