Discord bot /broadcast command in every server stops after 40~ servers without errors

Question

So i am trying to make a /broadcast command for my discord.py bot that will send a specific inserted message to every server it is into (only the bot owner can use it). I am using it to send updates and infos on error and so on. BUT... it stops after a certain amount of servers (40~) without any error, as it would have done his job and that would be all. Code keep running, /broadcast stops. I should even added a way to skip servers where it does not have permissions to write...

import discord
from discord.ext import commands
import asyncio  # Import asyncio for handling asynchronous tasks

# Define the intents for the bot
intents = discord.Intents.default()
intents.messages = True
intents.guilds = True

# Initialize the bot with the specified command prefix and intents
bot = commands.Bot(command_prefix="!", intents=intents)

# Define the broadcast command with owner-only access
@commands.is_owner()
@bot.hybrid_command(name="broadcast", description="Broadcast a message to specific channels")
async def broadcast(ctx, *, input_message: str):
    # Defer the response if the context is an interaction (for slash commands)
    if isinstance(ctx, discord.Interaction):
        await ctx.response.defer(ephemeral=True)

    # Initialize the message count
    message_count = 0
    # Define the list of allowed channel names
    allowed_channel_names = ['general-chat', 'spam-chat', 'chat-general', 'talk-general', 'chat-spam', 'talk-spam', 'chat-generale', 'bot-spam', 'bot-chat', 'bot-talk', 'bot-general', 'bot-generale','bot-test', 'bot-test-spam', 'bot-test-chat', 'bot-test-talk','spam-bot', 'spam-chat-general', 'spam-chat-talk', 'spam-chat-general-test','spam-shapes','shapes-spam', 'shapes-chat', 'shapes-talk', 'shapes-general', 'shapes-generale']

    # Iterate over all guilds the bot is a part of
    for guild in bot.guilds:
        # Iterate over all text channels in the guild
        for channel in guild.text_channels:
            # Check if the channel is in the allowed list and the bot has permission to send messages
            if channel.name in allowed_channel_names and channel.permissions_for(guild.me).send_messages:
                try:
                    # Send the input message to the channel
                    await channel.send(input_message)
                    message_count += 1
                    print(f"Message sent to: {channel.name} in {guild.name} (Count: {message_count})")
                except discord.HTTPException as e:
                    # Handle rate limiting by waiting and retrying
                    if e.status == 429:
                        print("Rate limited. Waiting to retry...")
                        await asyncio.sleep(e.retry_after)  # Wait for rate limit to expire before retrying
                        await channel.send(input_message)  # Retry sending the message
                    else:
                        print(f"An HTTPException occurred: {e}")
                except Exception as e:
                    # Handle any other exceptions that may occur
                    print(f"An error occurred when sending to {channel.name} in {guild.name}: {e}")
                    continue  # Ensures the bot continues with the next channel/server

    # Print the total number of messages sent after the broadcast is completed
    print(f"Broadcast completed. Total messages sent: {message_count}")

# Define the on_ready event to indicate the bot is ready and sync slash commands
@bot.event
async def on_ready():
    await bot.tree.sync()  # Syncs the command tree to enable slash commands
    print(f"Logged in as {bot.user.name}")

# Other parts of your code...

# Directly assign the bot token
token = "TOKEN"

# Ensure the token is not empty
if token == "":
    raise Exception("Please add your token to the code")

# Run the bot with exception handling
try:
    bot.run(token)
except discord.HTTPException as e:
    if e.status == 429:
        print("The Discord servers denied the connection for making too many requests.")
    else:
        print(f"An HTTPException occurred: {e}")
except Exception as e:
    print(f"An error occurred: {e}")