Mycoplasma is intrinsically resistant to:
Ref. Robbins Pathology. 9th edition. Page. 1375
 
Mycoplasma

Smallest extracellular bacteria.
Lack a cell wall; are very flexible and able to pass through filters which are 0.4 microns and which stop most bacteria.  
Contain sterols in their cell membrane; however, they cannot synthesize sterols so mycoplasmas acquire sterols from hosts or special media.  
Facultative anaerobes except for Mycoplasma pneumoniae, which is an obligate aerobe.  
Spread by direct contact or fresh respiratory droplets.  
Bind to the exterior of cells and damage epithelium from the outside.  
Fastidious and slow to grow even on special cholesterol-containing medium, so diagnosis  is usually clinical or serological with PCR becoming more readily available.  
Cold agglutinins (autoantibodies agglutinating red blood cells at 4°C) may be present after 1 to 2 weeks of clinical disease. Titers greater than 1:32 are generally considered positive.  Complement fixation is more sensitive.  
They are resistant to cephalosporin antibiotics
Mycoplasma pneumoniae causes respiratory tract infections.  
Mycoplasma hominis and Ureaplasma urealyticum appear to be involved in genitourinary tract infections
Aminogloycosides
Ceftazidime
Macrolides
Doxycycline