We have similar operating guidance for MHE in cold box for air separations plant, where exit temp for feed air is -160degC at 5kg/cm2 g - if dp across Main HE increases on feed air pass, then check the upstream mol sieves unit for CO2 breakthrough or the refrigeration unit further upstream for high exit temp (high water content).
Hence would guess there is water breakthrough in this gas stream to cold box MHE from your upstream drying system - how is gas dehydration done ?

Dehydration unit is working properly. But my question is dont you think the difference between allowable and calculated is very Narrow???

Increase from 0.3bar to 0.4bar is a 30% increase, which may be a reasonable gap to indicate start of water ice deposition in the MHE.
But calculated dp of 0.3bar would be at design flow; so is your flow at max design flow?
So are you injecting MeOH all the time now?
How do you know the dehydration unit is working as expected?

"Increase from 0.3bar to 0.4bar is a 30% increase."
Yes, but its just 0.1 bar increase!

"so is your flow at max design flow?"
No, we are working on 75% design capacity.

So are you injecting MeOH all the time now?
No, due to product pollution with methanol our management insist on not injecing methanol.

How do you know the dehydration unit is working as expected?
Based on feed gas dew point, it matches design criteria.

At 75% flow, dp should only be 0.3 x (0.75^2) = 0.17bar, so there clearly is something not right in the MHE on the feed gas pass.
What type of dehydration unit is it and what is its design exit dry gas dewpoint ?
It is often the case that water dewpoint measurements produced by inline dewpoint analysers is not correct - a lab analytical test is better

Lab analytical result: minus 90 C, for our natural gas!
You know that dew point is dependent on gas composition and pressure and temperature

Don't you think your are over Strict? 0.17 bar vs 0.3 Bar??!!!

Pressure drop varies as Q^2 ( Q = flowrate),so dp at 75% flow should be much lower than 0.3bar.
Ok so -90degC dewpoint is a lab test result - much more reliable. Such a water dewpoint can only be obtained with mol sieves operating in temperature swing mode (TSA).

Can only guess that the increase in dp is due to some abnormal operation in the upstream dehydration unit in the recent past, and that now, dewpoint has returned to normal. So there is no further deterioration in dp on feed gas cell in the cold box MHE ?

Guess there are only 2 options to clear this partial hydrate blockage in the MHE - (a) inject methanol in feedgas to dissolve the hydrates ( which your company does not wish to take up) (b) shutdown and defrost the cold box and MHE.

If there is a turbo expander downstream of the MHE for chilled feedgas, check if there is a risk of solid hydrates or ice from the MHE feedgas pass getting blown into expander casing (which could result in mechanical damage of the expander) if suddenly dislodged.