Mujica, 77, came to power amid optimism his easy-going patrician style of governance would boost business confidence, stabilize Uruguayan society and make the most of the country's commodities-driven income growth.
Instead, critics of Mujica complain that most of the country's economic and social problems remain unresolved and a runaway inflation is taking a toll on Uruguay's living standards.
Latest data indicate Uruguay's economy is slowing but remains on track for further growth.
Gross domestic product during the second quarter of 2012 increased 0.8 percent over the previous quarter and 3.8 percent over the same quarter a year ago, Central Bank data indicated.
Domestic demand has helped Uruguay sustain growth but imports expanded 13.2 percent, widening the trade deficit gap.
The president is also faulted for not standing up to alleged bullying by Argentine President Fernandez de Kirchner.
Mujica won international respect after he persuaded Fernandez to drop her confrontation with Uruguay over eucalyptus pulp processing, which Fernandez claimed was a major pollutant, an argument rejected by the International Court in The Hague, Netherlands.
After a brief "honeymoon," Uruguay's ties with Argentina soured again as Montevideo tried unsuccessfully to resolve differences over border tariffs, disputes over the use of waterways and other trade issues. Critics called his efforts ineffective, lacking assertive authority.
So far Mujica has dismissed opinion polls that show him in an increasingly poor light. But the growing unpopularity of the aging president has been cited by critics as a sign of weakness.
Analysts said approval ratings extracted from opinion polls produced after interviews with a few hundred people could still prove wrong and not affect Mujica's standing but popular perceptions about the president are changing the way Uruguayans regard his presidency.
Approval ratings for Mujica dropped to 36 percent, the lowest since he took office in March 2010, and the lowest of the ruling coalition Broad Front, latest data showed.
The opinion poll was done Aug. 31-Sept. 10 and involved telephone interviews with 800 people.
Mujica has dismissed the poll results, refusing to interpret the results. "My job is to keep working and that's it," Mujica was quoted as saying.
Although Uruguay's exports are booming, new import curbs in Argentina and Brazil are set to change the outlook and the country's international trade performance.
The Brazilian congress this week set in motion a bill which will enable the opening of tax free shops to compete against foreign imports.