OSError: [Errno 24] Too many open files - Async Programing in Python

I am all new to asynchronous programing in Python. I am enhancing part of my code to work asynchronously where the rest of the code works synchronously. The part I am enhancing asynchronously is to upload n number of files to a sftp and S3 bucket. The code I have written is working well for smaller sets of records, say like 100 to 300, but when the record set grows to 1000 or more, I am getting the following error "OSError: [Errno 24] Too many open files" for both uploading functions. Can anyone help me in general how the async works here and identify the issue?

I am using asyncssh and aiobotocore libraries for this code.

class my_class():

    def event_loop(self):

        tuple_of_records = () ##my files are kept in this tuple
        loop = asyncio.get_event_loop()
        loop.run_until_complete(self.iterate_asynchronously(tuple_of_records))
        loop.close()

    async def iterate_asynchronously(self,tuple_of_records): ##processing files in batch
        batch_size = 100
        batches = [tuple_of_records[i:i+batch_size] for i in range(0, len(tuple_of_records), batch_size)]

        batch_tasks = [self.batch_process(batch) for batch in batches]
        await asyncio.gather(*batch_tasks)

    async def batch_process(self,batch):
        tasks = [self.my_method(files) for files in batch]
        await asyncio.gather(*tasks)


    async my_method(self):
        await asyncio.gather(self.sftp_uploader(source_file,destination_file),self.s3_uploader(source_file,destination_file))

    async def sftp_uploader(self,source_file,destination_file)
        async with asyncssh.connect(
                host = "hostname",
                username = "uname",
                password = "pwd",
                known_hosts=None,) as sftp_connection: 
                async with sftp_connection.start_sftp_client() as sftp_client: 
             
            await sftp_client.put(source_file,destination_file)

    async def s3_uploader(self, source_file, destination_file): 
        ses = session.get_session()                    
        async with ses.create_client('s3', aws_secret_access_key = 'key', aws_access_key_id = 'id') as s3_client:
            with open(source_file, 'rb') as file:
                await s3_client.put_object(Bucket = 'bucket_name', Key = destination_file, Body=file)

if __name__ == "__main__":
    o = my_class()
    o.event_loop()

Here is the error I am receiving:

Traceback (most recent call last):
  File "My_code.py", line 455, in sftp_uploader
    async with asyncssh.connect(
  File "/usr/local/lib/python3.8/dist-packages/asyncssh/misc.py", line 220, in __aenter__
    self._result = await self._coro
  File "/usr/local/lib/python3.8/dist-packages/asyncssh/connection.py", line 6854, in connect
    return await _connect(options, loop, flags, conn_factory,
  File "/usr/local/lib/python3.8/dist-packages/asyncssh/connection.py", line 297, in _connect
    _, conn = await loop.create_connection(conn_factory, host, port,
  File "/usr/lib/python3.8/asyncio/base_events.py", line 1025, in create_connection
    raise exceptions[0]
  File "/usr/lib/python3.8/asyncio/base_events.py", line 1010, in create_connection
    sock = await self._connect_sock(
  File "/usr/lib/python3.8/asyncio/base_events.py", line 907, in _connect_sock
    sock = socket.socket(family=family, type=type_, proto=proto)
  File "/usr/lib/python3.8/socket.py", line 231, in __init__
    _socket.socket.__init__(self, family, type, proto, fileno)
OSError: [Errno 24] Too many open files