Output getting stuck

Hello Abaqus members, 
I am doing an explicit simulation of a simple fork and fiber system. The parts have a node to node connectivity. The fork is subjected to a sinusoidal load, and I am interested in the displacement at the tip of fiber. 

After running the job for a while, the output gets stuck, meaning step time of the simulation does not change. But the job continues to run till the end of wall time. Because the size of fiber is too small (diameter in microns), a fine mesh is desired. Online search showed that mass scaling may be an option to progress the simulation. It actually helped me to run the job without much change in percentage mass. However, the output again gets stuck- this time at a higher step time. I am clueless as to how the job can be successfully completed. I can not increase mass scaling further. I also checked all of my units, which I found are consistent (mm-SI unit system). 

I request you to please help me find the discrepancies, if any, in my file, or suggest a way to solve the problem. I need to get a steady state displacement. It is only after I increased my simulation time that this problem has started to show. I have pasted a part of one of my simulation status file here. 

 STEP 1  ORIGIN 0.0000 

              STEP     TOTAL       CPU      STABLE    CRITICAL    KINETIC      TOTAL    PERCENT 
INCREMENT     TIME      TIME      TIME   INCREMENT     ELEMENT     ENERGY     ENERGY  CHNG MASS 
 24739073  3.818E-03 3.818E-03  25:55:16 1.214E-10       65715  8.549E-08 -2.727E-09   0.000E+00 
 24765034  3.825E-03 3.825E-03  25:57:16 1.214E-10       65715  5.934E-08 -2.736E-09   0.000E+00 
 24766500  3.825E-03 3.825E-03  25:57:24 1.214E-10       65715  5.652E-08 -2.736E-09   0.000E+00 
ODB Field Frame Number     94 of    150 requested intervals at  3.824873E-03 
 24792379  3.831E-03 3.831E-03  25:59:23 1.214E-10       65715  8.935E-09 -2.738E-09   0.000E+00 
 24818029  3.837E-03 3.837E-03  26:01:23 1.214E-10       65715  6.651E-09 -2.739E-09   0.000E+00 
 24842696  3.843E-03 3.843E-03  26:03:23 1.214E-10       65715  4.962E-08 -2.740E-09   0.000E+00 
 24868625  3.849E-03 3.849E-03  26:05:23 1.214E-10       65715  8.392E-08 -2.748E-09   0.000E+00 
 24895274  3.855E-03 3.855E-03  26:07:23 1.214E-10       65715  6.049E-08 -2.757E-09   0.000E+00 
 24920377  3.861E-03 3.861E-03  26:09:23 1.214E-10       65715  1.308E-08 -2.759E-09   0.000E+00 
 24941262  3.866E-03 3.866E-03  26:10:59 1.214E-10       65715  8.883E-10 -2.759E-09   0.000E+00 
ODB Field Frame Number     95 of    150 requested intervals at  3.865563E-03 
 24967886  3.872E-03 3.872E-03  26:12:58 1.214E-10       65715  3.915E-08 -2.760E-09   0.000E+00 
 24991805  3.877E-03 3.877E-03  26:14:58 1.214E-10       65715  8.005E-08 -2.765E-09   0.000E+00 
 25015249  3.883E-03 3.883E-03  26:16:58 1.214E-10       65715  7.676E-08 -2.774E-09   0.000E+00 
 25039837  3.889E-03 3.889E-03  26:18:58 1.214E-10       65715  3.210E-08 -2.778E-09   0.000E+00 
 25064376  3.894E-03 3.894E-03  26:20:58 1.214E-10       65715  4.880E-10 -2.779E-09   0.000E+00 
 25089096  3.900E-03 3.900E-03  26:22:58 1.214E-10       65715  2.047E-08 -2.780E-09   0.000E+00 
 25113826  3.906E-03 3.906E-03  26:24:58 1.214E-10       65715  6.713E-08 -2.783E-09   0.000E+00 
 25138459  3.906E-03 3.906E-03  26:26:58 1.214E-10       65715  8.232E-08 -2.792E-09   0.000E+00 
 25163140  3.906E-03 3.906E-03  26:28:58 1.214E-10       65715  4.702E-08 -2.798E-09   0.000E+00 
 25187849  3.906E-03 3.906E-03  26:30:58 1.214E-10       65715  5.265E-09 -2.800E-09   0.000E+00 
 25212421  3.906E-03 3.906E-03  26:32:58 1.214E-10       65715  9.174E-09 -2.800E-09   0.000E+00 
 25237078  3.906E-03 3.906E-03  26:34:58 1.214E-10       65715  5.371E-08 -2.802E-09   0.000E+00 
 25261671  3.906E-03 3.906E-03  26:36:58 1.214E-10       65715  8.330E-08 -2.810E-09   0.000E+00 
 25286229  3.906E-03 3.906E-03  26:38:58 1.214E-10       65715  6.132E-08 -2.818E-09   0.000E+00 
 25310400  3.906E-03 3.906E-03  26:40:58 1.214E-10       65715  1.570E-08 -2.820E-09   0.000E+00 
 25337189  3.906E-03 3.906E-03  26:42:58 1.214E-10       65715  3.150E-09 -2.820E-09   0.000E+00 
 25362807  3.906E-03 3.906E-03  26:44:58 1.214E-10       65715  4.382E-08 -2.822E-09   0.000E+00 
 25387882  3.906E-03 3.906E-03  26:46:58 1.214E-10       65715  8.124E-08 -2.829E-09   0.000E+00 
 25412897  3.906E-03 3.906E-03  26:48:58 1.214E-10       65715  6.782E-08 -2.838E-09   0.000E+00 
 25438903  3.906E-03 3.906E-03  26:50:58 1.214E-10       65715  1.918E-08 -2.840E-09   0.000E+00 
 25464017  3.906E-03 3.906E-03  26:52:58 1.214E-10       65715  8.812E-10 -2.841E-09   0.000E+00 
 25489189  3.906E-03 3.906E-03  26:54:58 1.214E-10       65715  3.514E-08 -2.842E-09   0.000E+00 
 25514548  3.906E-03 3.906E-03  26:56:58 1.214E-10       65715  7.783E-08 -2.848E-09   0.000E+00 
 25540920  3.906E-03 3.906E-03  26:58:58 1.214E-10       65715  7.152E-08 -2.857E-09   0.000E+00 

Please help me out. Your feedback is highly appreciated. 
Thanks in advance! 

Mandar