Thank you for posting here.
Is this you ?

Все отлично. Только одна проблема - почему то не показывает более 45 эскизов, добавляешь новую закладку - и вместо эскизов значек обновления и все! В чем проблема?

Welcome to Userlogos !

The screenshot you have supplied is most helpful

A screenshot of your preferences/General would also be valuable.

Have not seen this problem ever before....

The first thing I would do temporarily is to disable ALL your other Addons/Extensions just to be certain there is no conflict

It would be important to know.
The cells that are blank are they cells with a logo ?
If they are could you try loading a known logo, that is one from a working cell higher up.

Could you also in the cells that are not working try putting temporarily a URL from a working cell.

This will create less variables.

You could also as an exercise start a New Firefox profile with the same number of cells and see if you can reproduce the problem.
But use only Logos and URLs that you know work.

If you do all this, this will help clarify hopefully what is or is not effecting your Fast Dial Page.

I apologise for asking you all these things, but something must be causing your problem and we need to find out what it is

If you are linking to a URL in a cell which is very slow, and you do not want to have a logo for that cell and the cell is refreshing endlessly, one can load a completely transparent logo.

In that way the cell will no longer be trying to look for the URL to create a thumbnail screenshot

You can download a blank fully transparent logo here

I do not speak or read Russian.....
Я не понимаю, Россия

English is better...

Hi, it's me...

Cells with missing images - these are sites that previously were
displayed as screenshots (thumbnails) of sites and also those, that have logo assigned.
ALL logos are stored on hard drive..
If you create a new bookmark with a site that's working, then image is shown.
If you create a new and assign a logo or load site screenshot then this problem appears.
Also appears when you click REFRESH button.

(thanks T for the translation)

Please try first in new Firefox Profile as mentioned above FIRST

If you wanted you could back up your present profile, full profile backup with FEBE.

This would be a security measure

I found the following in an old thread.
This procedure is based on the idea that preferences have got corrupted.
So this clears the settings before a reset.

Please try the following:

Go to preferences general
Hit defaults

Restart firefox and then reset your preferences again.

and then restart firefox again just to be sure

Found in old thread here

No promises

Thank you.

Really helped create a new profile in Firefox. At the moment, about 40 tabs created in the Fast Dial and no errors were found.

Good news !!!!

If you manage to get things working OK, the question I suppose remains to discover what was causing your error.

1.
Was it another extension ????
Test one at a time

2.
Were the preferences settings corrupted
Try reset defaults

3.
Just consider previous Profile corrupted and remain with new working profile and remove old one.

Really glad things are looking good....
Please keep us posted with your findings