Slow-acting trage fuse unexpectedly blowing
I strongly doubt that the datasheet is guaranteeing that the fuse won't blow for at least two minutes! Usually such curves are showing the worst-case blow times -- in other words, the fuse will blow within two minutes at most.

If your typical current is 111 mA, then your fuse should be rated for at least 200 mA. Or find a different way to limit the current.

Is this the fuse in question? Note that the datasheet only guarantees 200 ms minimum holding time between 1.5&times; and 2.75&times; overload.