Stored procedure with transaction, stops at transaction - sql-server

Question

So I have 5 PC's that run the same Stored Proc on 1 SQL server. For the sake of giving an example, let's say it's a program that runs over night. A PC executes a stored proc with an userID, and based on it, will update multiple tables in SQL Server. And this is done for all 2000 users in the company. However, as we have 5 PC's doing this, we are working with table-locks and transaction.
99% of the time, the stored proc works as intended, but every now and then, the SP just seems to stop before the transaction. Here is a breakdown of my SP:
CREATE PROCEDURE dbo.UpdateClient #UserID #PCID
(Declared variables etc)
BEGIN
BEGIN TRY
INSERT INTO dbo.log(event, PC_ID) values('The stored proc has been started by PC:', #PCID)
-- I have added these logging to my SP to try and find the issue but with no luck
BEGIN TRANSACTION T1
INSERT INTO dbo.log(event, PC_ID) values('Transaction has been opened', #PCID)
SELECT TOP 1 * FROM dbo.MasterTable with (tablockx, holdlock)
-- As we are having multiple PC's using the same SP at the same time,
-- we decided on using a table that is being read and locked when free by "the master" at that moment
INSERT INTO dbo.log(event, PC_ID) values('Master has been claimed', #PCID)
/**** Here we have a ton of UPDATE TABLE and INSERT INTO statements taking place ****/
INSERT INTO dbo.log(event, PC_ID) values('Tables have been updated', #PCID)
INSERT INTO dbo.log(event, PC_ID) values('Master role will be released', #PCID)
COMMIT TRANSACTION T1
END TRY
BEGIN CATCH
INSERT INTO dbo.log(event, PC_ID) values(CONCAT('An Error has occurred:',ERROR_MESSAGE()), #PCID)
END CATCH
INSERT INTO dbo.log(event, PC_ID) values('Stored procedure is now ending', #PCID)
END
Having these run by external PC's, makes it harder to log so the dbo.log is all I have in this case. As said before, sometimes the transaction doesn't get executed and then I end up with a log like this (let's say I only had PC1 and PC2 running that night):
ID| Event | PC_ID
1 | The stored proc has been started by PC: | PC1
2 | The stored proc has been started by PC: | PC2
3 | Transaction has been opened | PC2
4 | Master has been claimed | PC2
5 | Tables have been updated | PC2
6 | Master role will be released | PC2
7 | Stored procedure is now ending | PC2
8 | The stored proc has been started by PC: | PC1
9 | Transaction has been opened | PC1
etc
This is where I am lost. PC1 starts the Stored proc, but doesn't get further then the first log line. PC2, which started at the exact same time, did however go through the whole thing. My first thought was that (somehow) the transactions colide. But what I find weird is that PC1's SP doesn't even execute stuff outside the transaction. My CATCH statement nor the extra log line in the end of the SP are executed.
In the end, PC1 just executes it's next SP with a new UserID (but that ultimately breaks stuff in the end)
Any ideas/suggestion on how to fix this problem? As said before, 99% of the time it works but that 1% is causing a lot of issues.