The frightened condition is dependent on the source of fear being in line of sight. Do creatures with additional senses like blindsight, tremor sense and web sense find it extremely difficult to break line of sight?
Unless a term is defined in the rules it takes its normal English meaning.
From the free dictionary: line of sight is "An imaginary line from the eye to a perceived object." Things that block sight (like your eyelids) block line of sight.
What the Player's Handbook (p. 290) says is:
A frightened creature has disadvantage on ability checks and attack rolls while the source of its fear is within line of sight.
The creature can’t willingly move closer to the source of its fear.
Looking at each of the senses in the Monster Manual (p. 8-9):
A monster with blindsight can perceive its surroundings without relying on sight, within a specific radius.
Specifically, no "sight" is involved with blindsight so there is no "line of sight". Blindsight to the source dos not cause the disadvantage.
A monster with darkvision can see in the dark within a specific radius. The monster can see in dim light within the radius as if it were bright light, and in darkness as if it were dim light.
This uses "sight" and will cause disadvantage.
A monster with tremorsense can detect and pinpoint the origin of vibrations within a specific radius, provided that the monster and the source of the vibrations are in contact with the same ground or substance. Tremorsense can't be used to detect flying or incorporeal creatures.
No eyeballs used here so no disadvantage.
A monster with truesight can, out to a specific range, see in normal and magical darkness, see invisible creatures and objects, automatically detect visual iilusions and succeed on saving throws against them, and perceive the original form of a shapechanger or a creature that is transformed by magic. Furthermore, the monster can see into the Ethereal Plane within the same range.
You definitely don't want this if you are frightened.
Web sense is not a generic sense; that is it is specific to specific monsters and may not have the same effects. That said, it probably does have the same effects, I haven't checked. From the Ettercap on p. 131:
Web Sense. While in contact with a web, the ettercap knows the exact location of any other creature in contact with the same web.
There is no suggestion that it is using "sight" to do this so no disadvantage.