Urethritis: This is the most likely diagnosis due to the symptom of constant urethral burning, which is a common presentation of urethritis, an inflammation of the urethra often caused by infection.

Urinary Tract Infection (UTI): UTIs can cause burning sensations in the urethra, especially during urination, and if the infection is not fully cleared, it could lead to constant discomfort.
Prostatitis: In men, prostatitis (inflammation of the prostate gland) can cause urethral burning, among other symptoms like pelvic pain and difficulty urinating.
Vaginitis: In women, vaginitis (inflammation of the vagina) can sometimes cause a burning sensation in the urethra due to the close proximity of the vagina and urethra.

Sexually Transmitted Infections (STIs): Certain STIs like gonorrhea, chlamydia, and herpes can cause urethral burning. Missing these diagnoses could lead to serious complications, including infertility and increased risk of HIV transmission.
Interstitial Cystitis: A chronic condition causing bladder pressure, bladder pain, and sometimes urethral burning. It's crucial not to miss this diagnosis as it requires specific management and can significantly impact quality of life.
Urethral Stricture: A narrowing of the urethra caused by scar tissue, which can lead to obstructive urinary symptoms and urethral burning. Missing this diagnosis could lead to complications like urinary retention and kidney damage.

Urethral Carcinoma: Cancer of the urethra is rare but can cause urethral burning among other symptoms. Early detection is crucial for effective treatment.
Sjögren's Syndrome: An autoimmune disorder that can cause dryness in mucous membranes, including the urethra, leading to burning sensations. It's rare but important to consider in patients with other systemic symptoms.
Urethral Diverticulum: A condition where a pouch or pocket forms in the wall of the urethra, which can cause a variety of symptoms including urethral burning, especially if it becomes infected.