I struggle to fall asleep and wake up every few hours regardless of where I am. Zopiclone did not help much. What might be the problem?

Bad dreams. If you rule out the external causes mentioned by dr. Olson the remaining cause is waking during dreams. We go into rem sleep, in which we dream about every 2 hours at the beginning of the night and about every 75 minutes at the end of sleep. The bad dream may be awakening you without your remembering the dream at all. This is more likely if you awaken with a fast pulse. If so, see a therapist.
Sleep disorder. Non-restorative sleep/disrupted sleep can have many causes including: anxiety, restless leg syndrome/periodic leg movement disorder, apnea, bipolar affective disorder, secondary or primary insomnia, medications, stress, chronic pain, presence of a pesky pet, or partner's snoring. Look to these as potential causes and pursue treatment. Generic sleep remedy without finding the cause may disappoint.