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I have a tab-separated file that looks as follows:

$ cat file
GCF_000015405.1_ASM1540v1.dist_nbr_anntn WP_011558474.1 1159543 1160595 -4330977 polyketide synthase [Mycobacterium]
GCF_000015405.1_ASM1540v1.dist_nbr_anntn WP_011558475.1 1160607 1161116 12 isoprenylcysteine carboxyl methyltransferase [Mycobacterium]
GCF_000015405.1_ASM1540v1.dist_nbr_anntn WP_011558476.1 1161113 1162129 -3 NAD(P)/FAD-dependent oxidoreductase [Mycobacterium]
GCF_000015405.1_ASM1540v1.dist_nbr_anntn WP_011559726.1 2496640 2497560 1334511 polyketide synthase [Mycobacterium]
GCF_000015405.1_ASM1540v1.dist_nbr_anntn WP_011559727.1 2497568 2498122 8 isoprenylcysteine carboxyl methyltransferase [Mycobacterium]
GCF_000015405.1_ASM1540v1.dist_nbr_anntn WP_011562574.1 5526997 5528142 3028875 NAD(P)/FAD-dependent oxidoreductase [Mycobacterium]

I need to pick up successive lines that contain the keywords 'polyketide synthase', 'methyltransferase', and 'oxidoreductase' in that order, and write each of these sets into separate files for further analysis.

In this case, the input file would yield 2 output files which would look as follows:

$ cat file_1
GCF_000015405.1_ASM1540v1.dist_nbr_anntn WP_011558474.1 1159543 1160595 -4330977 polyketide synthase [Mycobacterium]
GCF_000015405.1_ASM1540v1.dist_nbr_anntn WP_011558475.1 1160607 1161116 12 isoprenylcysteine carboxyl methyltransferase [Mycobacterium]
GCF_000015405.1_ASM1540v1.dist_nbr_anntn WP_011558476.1 1161113 1162129 -3 NAD(P)/FAD-dependent oxidoreductase [Mycobacterium]

$ cat file_2
GCF_000015405.1_ASM1540v1.dist_nbr_anntn WP_011559726.1 2496640 2497560 1334511 polyketide synthase [Mycobacterium]
GCF_000015405.1_ASM1540v1.dist_nbr_anntn WP_011559727.1 2497568 2498122 8 isoprenylcysteine carboxyl methyltransferase [Mycobacterium]
GCF_000015405.1_ASM1540v1.dist_nbr_anntn WP_011562574.1 5526997 5528142 3028875 NAD(P)/FAD-dependent oxidoreductase [Mycobacterium]

I am having a hard time doing this using awk. Any suggestions?

P.S. I have other input files that contain variable number of instances of the keywords in successive lines. This is where I am getting stuck.

You can change what you are searching for as the script progresses and change where you write to each time you cycle through your terms

awk 'BEGIN 
 result_file = 1;
 term_id = 1;
 search_terms[1] = "polyketide synthase";
 search_terms[2] = "methyltransferase";
 search_terms[3] = "oxidoreductase"

$0 ~ search_terms[term_id] 
 print $0 >> FILENAME "_" result_file;
 term_id = term_id + 1;
 if (term_id > 3) 
 result_file = result_file + 1;
 term_id = 1
 
' input_file

This will write to input_file_1, input_file_2...

You might test the following code, where I split your keywords into an awk array named keys with N elements. everything starts with keys[1] and we set up a flag to check the next 1 to N-1 lines if they matches the corresponding values in the array keys [index from 2 to N], any mismatches before the N-1 line will reset this flag, if it reaches the N-1 line, then all are good for output (we also reset flag=0 here so a consecutive run of flag==1 never exceeds N-1 lines):

$ cat t24.awk
BEGIN 
 FS = OFS = "t";
 keywords = "polyketide synthase,methyltransferase,oxidoreductase";
 N = split(keywords, keys, ",")


# flag==1 means we are doing regex_match the next N-1 lines
# against corresponding array element in keys from [2:N] 
# once a unmatched found, turn off flag immediately
# if the flag==1 reached N-1 lines, then print the good match
flag 
 if($NF ~ keys[NR - start_line + 1]) 
 F = F ORS $0;
 if (NR == start_line+N-1) print F > "out_" f++; flag = 0 
 next
 else 
 flag = 0;
 


# set up the flag/start_line and reset F
$NF ~ keys[1] flag = 1; F = $0; start_line= NR; 

Run the above code with awk -f t24.awk file.txt. You can set up keywords (comma delimited) from your shell(instead of hard-coded in the BEGIN block), and then use -v keywords="..." to make it more flexible.